Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1476 conjugacy classes of subgroups; only the 353 normal subgroups are shown.
This group has 1476 conjugacy classes of subgroups — too many to draw. Only its 353 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. C22×C32×Q16 | C2 | semidirect |
| 4. C2×#63662 | C2 | semidirect |
| 5. #10592888 | C2 | direct (N × H) |
| 6. C2×#63644 | C2 | semidirect |
| 11. C2×C32×Q16 | C22 | semidirect |
| 21. #63662 | C22 | semidirect |
| 22. #63644 | C22 | semidirect |
| 23. C22×C3×Q16 | D3 | semidirect |
| 56. C2×C3×Q16 | C2×D3 | semidirect |
| 90. C22×Q16 | C3⋊D3 | semidirect |
| 134. C2×Q16 | C2×C3⋊D3 | semidirect |
| 168. C2×C32 | #470 | semidirect |
| 207. C32 | C2×#470 | semidirect |
| 230. C2×C3 | #5189 | semidirect |
| 246. C3 | C2×#5189 | semidirect |
| 248. C2 | #10592888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q16 | 2 |
| C2×#64155 | 2 |
| C22×#3743 | 2 |
| C2×#63662 | 2 |
| #10592888 | 2 |
| C2×#63644 | 2 |
| C2×#5189 | 3 |