Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
312 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 14. C2×Dic724 | C4 | semidirect |
| 15. C2×#15668439 | C4 | semidirect |
| 19. C2×Q16×C181 | C4 | semidirect |
| 49. C2×#10624382 | Q16 | semidirect |
| 88. C181 | #1969 | semidirect |
| 100. C2×Q16 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153885 | 2 |
| C2×#19153879 | 2 |
| C2×C8×#10624382 | 2 |
| (C2×#10624382)⋊Q8 | 2 |
| C2×Q16×D181 | 2 |
| #1969 | 181 |