Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1138 conjugacy classes of subgroups; only the 378 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 378 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×C4⋊#622 | C2 | direct (N × H) |
| 11. C4⋊#622 | C22 | direct (N × H) |
| 14. C22×C32×C4 | C8 | semidirect |
| 36. C2×C32×C4 | C2×C8 | semidirect |
| 60. C22×C32 | C4⋊C8 | semidirect |
| 65. C32×C4 | C22×C8 | semidirect |
| 91. C2×C32 | C2×C4⋊C8 | semidirect |
| 102. C22×C4 | #622 | semidirect |
| 118. C32 | C22×C4⋊C8 | semidirect |
| 130. C2×C4 | C2×#622 | semidirect |
| 137. C22 | C4⋊#622 | direct (N × H) |
| 146. C4 | C22×#622 | semidirect |
| 148. C2 | C2×C4⋊#622 | 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×C4⋊#622 | 2 |
| C22×C4⋊C8 | 9 |