Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
246 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 2. C2×#63371 | C2 | semidirect |
| 3. C2×C16×D9 | C2 | semidirect |
| 4. C9×C22⋊C16 | C2 | semidirect |
| 5. (C2×D9)⋊C16 | C2 | semidirect |
| 6. #10588179 | C2 | semidirect |
| 7. Dic9⋊C16 | C2 | semidirect |
| 47. C9⋊C16 | D4 | semidirect |
| 84. C22⋊C16 | D9 | semidirect |
| 111. C2×D9 | M32 | semidirect |
| 185. C9 | #2168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×#611 | 2 |
| C2×#63371 | 2 |
| C2×C16×D9 | 2 |
| C9×C22⋊C16 | 2 |
| (C2×D9)⋊C16 | 2 |
| #10588179 | 2 |
| Dic9⋊C16 | 2 |
| #69103 | 3 |