Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2626 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 2626 conjugacy classes of subgroups — too many to draw. Only its 463 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 |
|---|---|---|
| 1. C2×#64319 | C2 | semidirect |
| 2. C2×Q8×#157 | C2 | semidirect |
| 3. #10596525 | C2 | direct (N × H) |
| 4. C2×#64231 | C2 | semidirect |
| 5. C2×#64230 | C2 | semidirect |
| 6. C2×C4×GO+(4,𝔽2) | C2 | semidirect |
| 12. #64319 | C22 | semidirect |
| 16. Q8×#157 | C22 | semidirect |
| 21. #64231 | C22 | semidirect |
| 22. #64230 | C22 | semidirect |
| 23. C4×GO+(4,𝔽2) | C22 | semidirect |
| 32. C2×C32×Q8 | D4 | semidirect |
| 33. Q8×C3⋊D3 | D4 | semidirect |
| 36. C2×#634 | D4 | semidirect |
| 69. C2×#157 | #41 | semidirect |
| 74. C32×Q8 | C2×D4 | semidirect |
| 79. #634 | C2×D4 | semidirect |
| 126. #157 | C2×#41 | semidirect |
| 171. C2×C32 | #550 | semidirect |
| 173. C3⋊D3 | #550 | semidirect |
| 183. C2×Q8 | GO+(4,𝔽2) | semidirect |
| 220. C32 | C2×#550 | semidirect |
| 228. Q8 | C2×GO+(4,𝔽2) | semidirect |
| 273. C2 | #10596525 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64319 | 2 |
| C2×Q8×#157 | 2 |
| #10596525 | 2 |
| C2×#64231 | 2 |
| C2×#64230 | 2 |
| C2×C4×GO+(4,𝔽2) | 2 |
| C2×#550 | 9 |