Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
308 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. C2×#19153735 | C2 | semidirect |
| 5. #26041051 | C2 | semidirect |
| 6. #26041050 | C2 | semidirect |
| 7. C2×#101×C181 | C2 | semidirect |
| 108. C181 | #1915 | semidirect |
| 114. C2×#101 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042045 | 2 |
| #26041853 | 2 |
| #26041261 | 2 |
| C2×#19153735 | 2 |
| #26041051 | 2 |
| #26041050 | 2 |
| C2×#101×C181 | 2 |
| #1915 | 181 |