Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 2. #27133143 | C2 | semidirect |
| 3. #27132776 | C2 | semidirect |
| 4. #27132771 | C2 | semidirect |
| 5. C4×#15690276 | C2 | semidirect |
| 6. C2×#20259254 | C2 | semidirect |
| 7. #27132665 | C2 | semidirect |
| 8. #405×C191 | C2 | semidirect |
| 10. #20259344 | C4 | semidirect |
| 30. #15690287 | C2×C4 | semidirect |
| 37. Dic764 | C2×C4 | semidirect |
| 38. #15690276 | C2×C4 | semidirect |
| 39. D1528 | C2×C4 | semidirect |
| 47. C2×C8×C191 | C2×C4 | semidirect |
| 90. C191 | #2952 | semidirect |
| 99. #405 | D191 | semidirect |
| 133. C2×C8 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259344 | 2 |
| #27133143 | 2 |
| #27132776 | 2 |
| #27132771 | 2 |
| C4×#15690276 | 2 |
| C2×#20259254 | 2 |
| #27132665 | 2 |
| #405×C191 | 2 |
| #2952 | 191 |