Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
632 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 5. Q8×C22⋊C9 | C4 | semidirect |
| 21. (C22⋊C9)⋊C4 | Q8 | direct (N × H) |
| 83. C22⋊C9 | C4×Q8 | semidirect |
| 90. C22×Q8 | Dic9 | semidirect |
| 189. Q8 | (C22⋊C9)⋊C4 | direct (N × H) |
| 225. C22 | Q8×Dic9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C22⋊C9 | 2 |
| C4⋊((C22⋊C9)⋊C4) | 2 |
| C4×(C22⋊C9)⋊C4 | 2 |
| Q8×#217 | 3 |
| Q8×Dic9 | 4 |