Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1138 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 338 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×#63779 | C2 | direct (N × H) |
| 11. #63779 | C22 | direct (N × H) |
| 16. C22×C3⋊Dic3 | C8 | semidirect |
| 39. C2×C3⋊Dic3 | C2×C8 | semidirect |
| 60. C22×C32 | C4⋊C8 | semidirect |
| 67. C3⋊Dic3 | C22×C8 | semidirect |
| 91. C2×C32 | C2×C4⋊C8 | semidirect |
| 118. C32 | C22×C4⋊C8 | semidirect |
| 137. C22 | #63779 | direct (N × H) |
| 148. C2 | C2×#63779 | 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×C4×C3⋊Dic3 | 2 |
| C2×#63779 | 2 |
| C22×C4⋊C8 | 9 |