Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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. #26041934 | C2 | semidirect |
| 2. #26041631 | C2 | semidirect |
| 3. #26041614 | C2 | semidirect |
| 4. #26041556 | C2 | semidirect |
| 5. #26041523 | C2 | semidirect |
| 6. #26041484 | C2 | semidirect |
| 7. #26041422 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. #26041357 | C2 | semidirect |
| 10. #26041278 | C2 | semidirect |
| 11. #547×C181 | C2 | semidirect |
| 81. D724 | #41 | semidirect |
| 132. C181 | #3330 | semidirect |
| 135. #547 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041934 | 2 |
| #26041631 | 2 |
| #26041614 | 2 |
| #26041556 | 2 |
| #26041523 | 2 |
| #26041484 | 2 |
| #26041422 | 2 |
| C4×#15668434 | 2 |
| #26041357 | 2 |
| #26041278 | 2 |
| #547×C181 | 2 |
| #3330 | 181 |