Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
598 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C8×#157 | C2 | semidirect |
| 4. C4⋊C4×#157 | C2 | semidirect |
| 6. #10590182 | C2 | semidirect |
| 7. #10590163 | C2 | semidirect |
| 12. D4×#157 | C4 | semidirect |
| 20. #63782 | C4 | semidirect |
| 23. C32×#102 | C4 | semidirect |
| 24. #63659 | C4 | semidirect |
| 25. #63648 | C4 | semidirect |
| 26. #63636 | C4 | semidirect |
| 50. C4⋊#157 | C2×C4 | semidirect |
| 55. #3787 | C2×C4 | semidirect |
| 56. C2×C32×C8 | C2×C4 | semidirect |
| 57. C32×C4⋊C4 | C2×C4 | semidirect |
| 58. C4⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 60. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 94. C32×D4 | C42 | semidirect |
| 102. C4⋊(C3⋊D3) | C42 | semidirect |
| 156. #157 | #102 | direct (N × H) |
| 179. #102 | #157 | direct (N × H) |
| 241. C2×C8 | C2×#157 | semidirect |
| 248. C4⋊C4 | C2×#157 | semidirect |
| 276. C32 | C4×#102 | semidirect |
| 291. D4 | C4×#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#157 | 2 |
| C2×#63782 | 2 |
| C2×C8×#157 | 2 |
| C4⋊C4×#157 | 2 |
| C3⋊D3×#102 | 2 |
| #10590182 | 2 |
| #10590163 | 2 |
| C4×#102 | 9 |