Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
146 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 57 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. #27164136 | C2 | semidirect |
| 3. #27163847 | C2 | semidirect |
| 4. #27163825 | C2 | semidirect |
| 5. #27163824 | C2 | semidirect |
| 6. C4×C199⋊C16 | C2 | semidirect |
| 7. #443×C199 | C2 | semidirect |
| 10. #20263901 | C4 | semidirect |
| 11. #20263899 | C4 | semidirect |
| 12. #20263898 | C4 | semidirect |
| 13. #20263896 | C4 | semidirect |
| 71. C199 | #2178 | semidirect |
| 75. #443 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164448 | 2 |
| #27164136 | 2 |
| #27163847 | 2 |
| #27163825 | 2 |
| #27163824 | 2 |
| C4×C199⋊C16 | 2 |
| #443×C199 | 2 |
| #2178 | 199 |