Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 217 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×Q16×C3⋊D3 | C2 | semidirect |
| 3. C2×C32×SD32 | C2 | semidirect |
| 4. C2×#63656 | C2 | semidirect |
| 5. C2×#63654 | C2 | semidirect |
| 6. #10592614 | C2 | direct (N × H) |
| 7. C2×#63628 | C2 | semidirect |
| 8. C2×#63625 | C2 | semidirect |
| 17. Q16×C3⋊D3 | C22 | semidirect |
| 23. C32×SD32 | C22 | semidirect |
| 25. #63656 | C22 | semidirect |
| 26. #63654 | C22 | semidirect |
| 28. #63628 | C22 | semidirect |
| 29. #63625 | C22 | semidirect |
| 32. C2×C3×SD32 | D3 | semidirect |
| 81. C3×SD32 | C2×D3 | semidirect |
| 118. C2×SD32 | C3⋊D3 | semidirect |
| 176. SD32 | C2×C3⋊D3 | semidirect |
| 205. C2×C32 | #510 | semidirect |
| 248. C32 | C2×#510 | semidirect |
| 274. C2×C3 | #4915 | semidirect |
| 288. C3 | C2×#4915 | semidirect |
| 291. C2 | #10592614 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×C3⋊D3 | 2 |
| C2×#64121 | 2 |
| C2×C32×SD32 | 2 |
| C2×#63656 | 2 |
| C2×#63654 | 2 |
| #10592614 | 2 |
| C2×#63628 | 2 |
| C2×#63625 | 2 |
| C2×#4915 | 3 |