Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
988 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 988 conjugacy classes of subgroups — too many to draw. Only its 549 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 |
|---|---|---|
| 1. #26042005 | C2 | semidirect |
| 2. #26041988 | C2 | semidirect |
| 3. #26041907 | C2 | semidirect |
| 4. #26041836 | C2 | semidirect |
| 5. C2×#19153808 | C2 | semidirect |
| 39. #41×C181 | Q8 | semidirect |
| 74. C181 | #3504 | semidirect |
| 103. #41 | Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042005 | 2 |
| #26041988 | 2 |
| #26041907 | 2 |
| #26041836 | 2 |
| C2×#19153808 | 2 |
| #26041762 | 2 |
| C4×#41×C181 | 2 |
| #3504 | 181 |