Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #26041681 | C2 | semidirect |
| 3. #26041621 | C2 | semidirect |
| 4. #26041615 | C2 | semidirect |
| 5. #26041587 | C2 | semidirect |
| 6. #26041537 | C2 | semidirect |
| 7. C4×Dic724 | C2 | semidirect |
| 8. #26041321 | C2 | semidirect |
| 96. C181 | #3352 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041969 | 2 |
| #26041681 | 2 |
| #26041621 | 2 |
| #26041615 | 2 |
| #26041587 | 2 |
| #26041537 | 2 |
| C4×Dic724 | 2 |
| #26041321 | 2 |
| #436×C181 | 2 |
| #3352 | 181 |