Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #26041933 | C2 | semidirect |
| 2. #26041932 | C2 | semidirect |
| 3. #26041631 | C2 | semidirect |
| 4. #26041616 | C2 | semidirect |
| 5. #26041526 | C2 | semidirect |
| 6. #26041485 | C2 | semidirect |
| 7. #26041425 | C2 | semidirect |
| 8. C4×#15668434 | C2 | semidirect |
| 9. #26041356 | C2 | semidirect |
| 10. #26041277 | C2 | semidirect |
| 11. #474×C181 | C2 | semidirect |
| 99. D4×C181 | #41 | semidirect |
| 132. C181 | #3330 | semidirect |
| 138. #474 | D181 | semidirect |
| 222. D4 | #15668450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041933 | 2 |
| #26041932 | 2 |
| #26041631 | 2 |
| #26041616 | 2 |
| #26041526 | 2 |
| #26041485 | 2 |
| #26041425 | 2 |
| C4×#15668434 | 2 |
| #26041356 | 2 |
| #26041277 | 2 |
| #474×C181 | 2 |
| #3330 | 181 |