Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Fitting | C4×D4×C47 | C2 |
| hypercenter | C4×D4 | D47 |
| hypocenter | C47 | #546 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625350 | C2 | semidirect |
| 2. C22×D188 | C2 | semidirect |
| 3. #13094012 | C2 | semidirect |
| 4. #13094009 | C2 | semidirect |
| 5. #13094003 | C2 | semidirect |
| 6. #13093998 | C2 | semidirect |
| 7. #13093997 | C2 | semidirect |
| 8. #13093992 | C2 | semidirect |
| 9. C4×D188 | C2 | semidirect |
| 10. C22⋊C4×D47 | C2 | semidirect |
| 11. C4×D4×C47 | C2 | semidirect |
| 15. C22×C4×C47 | C22 | semidirect |
| 16. C2×C22⋊D47 | C22 | semidirect |
| 17. C2×C22⋊D47 | C22 | semidirect |
| 23. C2×C4×D47 | C22 | semidirect |
| 24. C2×C4×D47 | C22 | semidirect |
| 25. C2×Dic94 | C22 | semidirect |
| 26. C4⋊C4×C47 | C22 | semidirect |
| 28. C22⋊C4×C47 | C22 | semidirect |
| 29. C42×C47 | C22 | semidirect |
| 31. (C2×D47)⋊C4 | C22 | semidirect |
| 32. (C2×D47)⋊C4 | C22 | semidirect |
| 33. (C2×D47)⋊C4 | C22 | semidirect |
| 34. (C2×D47)⋊C4 | C22 | semidirect |
| 35. C4⋊Dic47 | C22 | semidirect |
| 36. Dic47⋊C4 | C22 | semidirect |
| 58. D188 | D4 | semidirect |
| 67. C22×C47 | #41 | semidirect |
| 91. C47 | #546 | semidirect |
| 101. C4×D4 | D47 | semidirect |
| 116. C22×C4 | C2×D47 | semidirect |
| 119. C4⋊C4 | C2×D47 | semidirect |
| 126. C22⋊C4 | C2×D47 | semidirect |
| 127. C42 | C2×D47 | semidirect |
| 165. C22 | #10625350 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625350 | 2 |
| C22×D188 | 2 |
| #13094012 | 2 |
| #13094009 | 2 |
| #13094003 | 2 |
| #13093998 | 2 |
| #13093997 | 2 |
| #13093992 | 2 |
| C4×D188 | 2 |
| C22⋊C4×D47 | 2 |
| C4×D4×C47 | 2 |
| #546 | 47 |