Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
978 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 978 conjugacy classes of subgroups — too many to draw. Only its 194 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×#3792 | C2 | semidirect |
| 3. C2×C22⋊#622 | C2 | semidirect |
| 4. #10593821 | C2 | direct (N × H) |
| 5. C2×C4⋊#622 | C2 | semidirect |
| 6. C2×C4×#622 | C2 | semidirect |
| 10. C2×#3792 | C22 | semidirect |
| 19. C22⋊#622 | C22 | semidirect |
| 20. C4⋊#622 | C22 | semidirect |
| 21. C4×#622 | C22 | semidirect |
| 37. C2×#622 | D4 | semidirect |
| 59. C2×C32×C4 | M16 | semidirect |
| 74. #622 | C2×D4 | semidirect |
| 104. C32×C4 | C2×M16 | semidirect |
| 145. C2×C32 | #436 | semidirect |
| 185. C32 | C2×#436 | semidirect |
| 203. C2×C4 | #3792 | semidirect |
| 226. C4 | C2×#3792 | semidirect |
| 229. C2 | #10593821 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3792 | 2 |
| C2×D4×C3⋊Dic3 | 2 |
| C2×C22⋊#622 | 2 |
| #10593821 | 2 |
| C2×C4⋊#622 | 2 |
| C2×C4×#622 | 2 |
| C2×#436 | 9 |