Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
330 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 74 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. D4×#622 | C2 | semidirect |
| 3. D4⋊#622 | C2 | semidirect |
| 4. #10590171 | C2 | semidirect |
| 5. C8×#622 | C2 | semidirect |
| 24. C32×D8 | C8 | semidirect |
| 38. C32×D4 | C2×C8 | semidirect |
| 48. #622 | D8 | direct (N × H) |
| 49. C32×C8 | C2×C8 | semidirect |
| 101. D8 | #622 | direct (N × H) |
| 122. C32 | C8×D8 | semidirect |
| 125. D4 | C2×#622 | semidirect |
| 137. C8 | C2×#622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#622 | 2 |
| D8×C3⋊Dic3 | 2 |
| D4⋊#622 | 2 |
| #10590171 | 2 |
| C8×#622 | 2 |
| C8×D8 | 9 |