Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 5. #10593536 | C2 | semidirect |
| 6. #10593535 | C2 | semidirect |
| 7. #10593534 | C2 | semidirect |
| 8. #10593533 | C2 | semidirect |
| 29. C2×#622 | Q8 | semidirect |
| 35. #3787 | Q8 | semidirect |
| 40. C2×C32×C8 | Q8 | semidirect |
| 41. C2×C3⋊(C3⋊C8) | Q8 | semidirect |
| 42. C8×C3⋊D3 | Q8 | semidirect |
| 43. C8×C3⋊D3 | Q8 | semidirect |
| 135. C2×C8 | PSU(3,𝔽2) | semidirect |
| 152. C32 | #3160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596542 | 2 |
| #10593768 | 2 |
| C2×C8×#157 | 2 |
| #10593543 | 2 |
| #10593536 | 2 |
| #10593535 | 2 |
| #10593534 | 2 |
| #10593533 | 2 |
| #3160 | 9 |