Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1018 conjugacy classes of subgroups; only the 287 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 287 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 |
|---|---|---|
| 3. C2×#63743 | C2 | direct (N × H) |
| 6. C22×#622 | C4 | semidirect |
| 10. #63743 | C22 | direct (N × H) |
| 19. C2×#622 | C2×C4 | semidirect |
| 40. #622 | C22×C4 | semidirect |
| 55. C22×C32 | #107 | semidirect |
| 84. C2×C32 | C2×#107 | semidirect |
| 109. C32 | C22×#107 | semidirect |
| 126. C22 | #63743 | direct (N × H) |
| 136. C2 | C2×#63743 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#622 | 2 |
| C22×#3724 | 2 |
| C2×#63743 | 2 |
| C22×#107 | 9 |