Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #27133131 | C2 | semidirect |
| 3. #27132774 | C2 | semidirect |
| 4. #27132769 | C2 | semidirect |
| 5. #27132762 | C2 | semidirect |
| 6. #27132657 | C2 | semidirect |
| 7. C2×#20259232 | C2 | semidirect |
| 8. #427×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 |
| 48. C2×C8×C191 | C2×C4 | semidirect |
| 89. C191 | #2943 | semidirect |
| 96. #427 | 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 |
| #27133131 | 2 |
| #27132774 | 2 |
| #27132769 | 2 |
| #27132762 | 2 |
| #27132657 | 2 |
| C2×#20259232 | 2 |
| #427×C191 | 2 |
| #2943 | 191 |