Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
444 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 21. Q8×Dic181 | C4 | semidirect |
| 22. C4×Dic362 | C4 | semidirect |
| 23. C4×Dic362 | C4 | semidirect |
| 24. #19153781 | C4 | semidirect |
| 25. #19153781 | C4 | semidirect |
| 30. C4×Q8×C181 | C4 | semidirect |
| 115. C181 | #2320 | semidirect |
| 131. C4×Q8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| (C2×#10624382)⋊Q8 | 2 |
| #26042230 | 2 |
| #26042228 | 2 |
| #26042224 | 2 |
| #26042223 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042215 | 2 |
| C4×Q8×D181 | 2 |
| #2320 | 181 |