Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 11. #19153816 | C4 | semidirect |
| 15. Q8×Dic181 | C4 | semidirect |
| 19. C4⋊Q8×C181 | C4 | semidirect |
| 75. C181 | #1506 | semidirect |
| 82. C4⋊Q8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042301 | 2 |
| #26042215 | 2 |
| #26042133 | 2 |
| #26041834 | 2 |
| #1506 | 181 |