Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
900 conjugacy classes of subgroups; only the 558 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 558 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×#63377 | C2 | direct (N × H) |
| 7. C22×C8×C9 | C4 | semidirect |
| 11. #63377 | C22 | direct (N × H) |
| 22. C2×C8×C9 | C2×C4 | semidirect |
| 44. C8×C9 | C22×C4 | semidirect |
| 59. C22×C9 | #106 | semidirect |
| 69. C22×C8 | Dic9 | semidirect |
| 85. C2×C9 | C2×#106 | semidirect |
| 95. C2×C8 | C2×Dic9 | semidirect |
| 107. C9 | C22×#106 | semidirect |
| 118. C8 | C22×Dic9 | semidirect |
| 122. C22 | #63377 | direct (N × H) |
| 131. C2 | C2×#63377 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C9 | 2 |
| C22×C4⋊Dic9 | 2 |
| C2×#63377 | 2 |
| C22×#817 | 3 |