Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
598 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 207 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×#63748 | C2 | direct (N × H) |
| 11. #63748 | C22 | direct (N × H) |
| 54. C22×C32 | #108 | semidirect |
| 85. C2×C32 | C2×#108 | semidirect |
| 110. C32 | C22×#108 | semidirect |
| 132. C22 | #63748 | direct (N × H) |
| 143. C2 | C2×#63748 | 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 |
| C23×#622 | 2 |
| C2×#63748 | 2 |
| C22×#108 | 9 |