Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
172 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 70 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. #15668433 | C8 | semidirect |
| 29. M16×C181 | C8 | semidirect |
| 66. C181 | #1278 | semidirect |
| 88. M16 | #13089685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042295 | 2 |
| C2×C4×#13089685 | 2 |
| M16×Dic181 | 2 |
| #1278 | 181 |