Finite Group DatabasebetaFinite Group DatabasebetaOrder 23488.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26044309 | C2 | semidirect |
| 2. #26044308 | C2 | semidirect |
| 3. #26044294 | C2 | semidirect |
| 4. #26044293 | C2 | semidirect |
| 5. #26044290 | C2 | semidirect |
| 6. #26044282 | C2 | semidirect |
| 7. #26044281 | C2 | semidirect |
| 8. C2×#19154567 | C2 | semidirect |
| 9. Q16×D367 | C2 | semidirect |
| 10. #26044269 | C2 | semidirect |
| 11. #137×C367 | C2 | semidirect |
| 87. C367 | #578 | semidirect |
| 94. #137 | D367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26044309 | 2 |
| #26044308 | 2 |
| #26044294 | 2 |
| #26044293 | 2 |
| #26044290 | 2 |
| #26044282 | 2 |
| #26044281 | 2 |
| C2×#19154567 | 2 |
| Q16×D367 | 2 |
| #26044269 | 2 |
| #137×C367 | 2 |
| #578 | 367 |