Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D47 |
| commutator, socle, cosocle | C22×C47 | C24 |
| Frattini | C22 | C23×D47 |
| Fitting | C23×C4×C47 | C2 |
| hypercenter | C23×C4 | D47 |
| hypocenter | C47 | #525 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ C23×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625350 | C2 | semidirect |
| 2. #13094007 | C2 | semidirect |
| 3. #13094003 | C2 | semidirect |
| 4. #13093998 | C2 | semidirect |
| 5. #13093993 | C2 | semidirect |
| 6. C4×C22⋊D47 | C2 | semidirect |
| 7. #13093983 | C2 | semidirect |
| 8. C23×C4×C47 | C2 | semidirect |
| 18. C2×D188 | C22 | semidirect |
| 19. C2×C4×D47 | C22 | semidirect |
| 20. C2×Dic94 | C22 | semidirect |
| 23. (C2×D47)⋊C4 | C22 | semidirect |
| 24. C4⋊Dic47 | C22 | semidirect |
| 25. Dic47⋊C4 | C22 | semidirect |
| 26. C4×Dic47 | C22 | semidirect |
| 35. C2×C4×C47 | D4 | semidirect |
| 51. C22×C47 | #41 | semidirect |
| 66. C47 | #525 | semidirect |
| 68. C23×C4 | D47 | semidirect |
| 108. C2×C4 | C22⋊D47 | semidirect |
| 118. 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 |
| #13094007 | 2 |
| #13094003 | 2 |
| #13093998 | 2 |
| #13093993 | 2 |
| C4×C22⋊D47 | 2 |
| #13093983 | 2 |
| C23×C4×C47 | 2 |
| #525 | 47 |