Finite Group DatabasebetaFinite Group DatabasebetaOrder 3008.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 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 | #117×C47 | C2 |
| hypercenter | #117 | D47 |
| hypocenter | C47 | #525 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10625350 | C2 | semidirect |
| 2. C22×C4×D47 | C2 | semidirect |
| 3. #13094008 | C2 | semidirect |
| 4. #13094004 | C2 | semidirect |
| 5. #13093999 | C2 | semidirect |
| 6. #13093994 | C2 | semidirect |
| 7. C4×D188 | C2 | semidirect |
| 8. #117×C47 | C2 | semidirect |
| 15. C2×D188 | C22 | semidirect |
| 19. C2×C4×D47 | C22 | semidirect |
| 20. C2×Dic94 | C22 | semidirect |
| 21. C4⋊C4×C47 | C22 | semidirect |
| 23. C42×C47 | C22 | semidirect |
| 25. (C2×D47)⋊C4 | C22 | semidirect |
| 26. C4⋊Dic47 | C22 | semidirect |
| 32. C2×C4×C47 | D4 | semidirect |
| 54. C2×D47 | #41 | semidirect |
| 66. C47 | #525 | semidirect |
| 74. #117 | D47 | semidirect |
| 88. C4⋊C4 | C2×D47 | semidirect |
| 92. C42 | C2×D47 | semidirect |
| 108. C2×C4 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10625350 | 2 |
| C22×C4×D47 | 2 |
| #13094008 | 2 |
| #13094004 | 2 |
| #13093999 | 2 |
| #13093994 | 2 |
| C4×D188 | 2 |
| #117×C47 | 2 |
| #525 | 47 |