Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#20259329 | C2 | semidirect |
| 2. #27132785 | C2 | semidirect |
| 3. #27132780 | C2 | semidirect |
| 4. #27132712 | C2 | semidirect |
| 5. #27132680 | C2 | semidirect |
| 6. #27132621 | C2 | semidirect |
| 10. #20259329 | C22 | semidirect |
| 11. #20259329 | C22 | semidirect |
| 17. #20259258 | C22 | semidirect |
| 18. #20259249 | C22 | semidirect |
| 19. #20259232 | C22 | semidirect |
| 20. C8×Dic191 | C22 | semidirect |
| 22. #137×C191 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C191 | C4 | semidirect |
| 89. C191 | #2955 | semidirect |
| 99. #137 | Dic191 | semidirect |
| 100. AGL(1,ℤ/8) | Dic191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259329 | 2 |
| #27132785 | 2 |
| #27132780 | 2 |
| #27132712 | 2 |
| #27132680 | 2 |
| #27132621 | 2 |
| #575×C191 | 2 |
| #2955 | 191 |