Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
440 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 234 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. #26042328 | C2 | direct (N × H) |
| 23. C2×#13089685 | Q8 | semidirect |
| 27. C2×Dic362 | C8 | semidirect |
| 42. #13089685 | C2×Q8 | semidirect |
| 43. Dic362 | C2×C8 | semidirect |
| 68. C2×C181 | C8×Q8 | semidirect |
| 72. C181 | C2×C8×Q8 | semidirect |
| 141. C2 | #26042328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042328 | 2 |
| C2×#19153883 | 2 |
| C2×C4⋊#13089685 | 2 |
| C2×C4×#13089685 | 2 |
| C2×#19153781 | 2 |
| C2×C8×Q8 | 181 |