Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1317 conjugacy classes of subgroups; only the 252 normal subgroups are shown.
This group has 1317 conjugacy classes of subgroups — too many to draw. Only its 252 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×Q8×C3⋊Dic3 | C2 | semidirect |
| 2. C22×C3×#215 | C2 | semidirect |
| 4. #10591622 | C2 | direct (N × H) |
| 5. C2×#63572 | C2 | semidirect |
| 6. C2×#63563 | C2 | semidirect |
| 13. Q8×C3⋊Dic3 | C22 | semidirect |
| 19. C2×C3×#215 | C22 | semidirect |
| 23. #63572 | C22 | semidirect |
| 24. #63563 | C22 | semidirect |
| 28. C22×#215 | D3 | semidirect |
| 37. C2×C32×Q8 | D4 | semidirect |
| 76. C2×#215 | C2×D3 | semidirect |
| 98. C32×Q8 | C2×D4 | semidirect |
| 108. C2×C3⋊Dic3 | SD16 | semidirect |
| 131. C2×C3×Q8 | #67 | semidirect |
| 187. C3⋊Dic3 | C2×SD16 | semidirect |
| 220. C3×Q8 | C2×#67 | semidirect |
| 255. C2×C32 | #460 | semidirect |
| 263. C2×Q8 | #625 | semidirect |
| 317. C32 | C2×#460 | semidirect |
| 325. Q8 | C2×#625 | semidirect |
| 349. C2×C3 | #5163 | semidirect |
| 370. C3 | C2×#5163 | semidirect |
| 372. C2 | #10591622 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊Dic3 | 2 |
| C22×C3×#215 | 2 |
| C2×#63914 | 2 |
| #10591622 | 2 |
| C2×#63572 | 2 |
| C2×#63563 | 2 |
| C2×#5163 | 3 |