Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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. #27133220 | C2 | semidirect |
| 2. #27133035 | C2 | semidirect |
| 3. #27133009 | C2 | semidirect |
| 4. #27132860 | C2 | semidirect |
| 5. #27132814 | C2 | semidirect |
| 6. #27132716 | C2 | semidirect |
| 8. C2×#15690275 | C22 | semidirect |
| 9. #20259322 | C22 | semidirect |
| 10. #20259322 | C22 | semidirect |
| 15. C4×Dic382 | C22 | semidirect |
| 17. C4⋊(C191⋊C8) | C22 | semidirect |
| 18. #20259243 | C22 | semidirect |
| 20. C4×C191⋊C8 | C22 | semidirect |
| 76. C2×C4×C191 | SD16 | semidirect |
| 104. C191 | #3208 | semidirect |
| 180. C2×C4 | #15690275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27133220 | 2 |
| #27133035 | 2 |
| #27133009 | 2 |
| #27132860 | 2 |
| #27132814 | 2 |
| #27132716 | 2 |
| C2×#127×C191 | 2 |
| #3208 | 191 |