Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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. #27164453 | C2 | semidirect |
| 2. C2×#20263896 | C2 | semidirect |
| 3. #27164288 | C2 | semidirect |
| 4. #27163831 | C2 | semidirect |
| 5. #27163825 | C2 | semidirect |
| 6. #27163802 | C2 | semidirect |
| 7. #576×C199 | C2 | semidirect |
| 9. C2×D1592 | C22 | semidirect |
| 13. #20263895 | C22 | semidirect |
| 14. C2×C199⋊C16 | C22 | semidirect |
| 15. #20263891 | C22 | semidirect |
| 93. C199 | #2192 | semidirect |
| 95. #576 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164453 | 2 |
| C2×#20263896 | 2 |
| #27164288 | 2 |
| #27163831 | 2 |
| #27163825 | 2 |
| #27163802 | 2 |
| #576×C199 | 2 |
| #2192 | 199 |