Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#15690288 | C2 | semidirect |
| 3. #27132776 | C2 | semidirect |
| 4. #27132774 | C2 | semidirect |
| 5. #27132770 | C2 | semidirect |
| 6. #27132766 | C2 | semidirect |
| 7. #27132761 | C2 | semidirect |
| 8. #27132698 | C2 | semidirect |
| 9. #27132658 | C2 | semidirect |
| 10. #97×D191 | C2 | semidirect |
| 11. #441×C191 | C2 | semidirect |
| 13. #20259345 | C4 | semidirect |
| 41. #15690288 | C2×C4 | semidirect |
| 49. #15690274 | C2×C4 | semidirect |
| 50. D1528 | C2×C4 | semidirect |
| 54. C8×D191 | C2×C4 | semidirect |
| 65. Q16×C191 | C2×C4 | semidirect |
| 114. C191 | #2943 | semidirect |
| 121. #441 | D191 | semidirect |
| 165. Q16 | C4×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20259345 | 2 |
| C4×#15690288 | 2 |
| #27132776 | 2 |
| #27132774 | 2 |
| #27132770 | 2 |
| #27132766 | 2 |
| #27132761 | 2 |
| #27132698 | 2 |
| #27132658 | 2 |
| #97×D191 | 2 |
| #441×C191 | 2 |
| #2943 | 191 |