Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
440 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 253 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. #26041403 | C2 | direct (N × H) |
| 21. C2×Dic362 | C8 | semidirect |
| 26. C2×#13089678 | Q8 | semidirect |
| 40. Dic362 | C2×C8 | semidirect |
| 46. #13089678 | C2×Q8 | semidirect |
| 68. C2×C181 | C8×Q8 | semidirect |
| 72. C181 | C2×C8×Q8 | semidirect |
| 141. C2 | #26041403 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic362 | 2 |
| #26041403 | 2 |
| C2×#19153745 | 2 |
| C2×C4×#13089678 | 2 |
| C2×C8×Dic181 | 2 |
| C2×C4⋊C8×C181 | 2 |
| C2×C8×Q8 | 181 |