Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
628 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 290 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 |
|---|---|---|
| 6. Q8×#10624382 | C4 | semidirect |
| 14. Q8×Dic181 | C4 | semidirect |
| 15. C4×Dic362 | C4 | semidirect |
| 16. #19153781 | C4 | semidirect |
| 19. C4×Q8×C181 | C4 | semidirect |
| 45. Dic362 | C42 | semidirect |
| 53. Q8×C181 | C42 | semidirect |
| 75. C181 | #2276 | semidirect |
| 87. C4×Q8 | #10624382 | semidirect |
| 116. Q8 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| C4⋊C4×#10624382 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26042215 | 2 |
| C4×Q8×D181 | 2 |
| #2276 | 181 |