Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
220 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 49 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. #27164823 | C2 | semidirect |
| 2. #27164454 | C2 | semidirect |
| 3. C2×#20263896 | C2 | semidirect |
| 4. #27163830 | C2 | semidirect |
| 5. #27163824 | C2 | semidirect |
| 6. #27163802 | C2 | semidirect |
| 7. #472×C199 | C2 | semidirect |
| 18. #20263895 | C22 | semidirect |
| 19. C2×C199⋊C16 | C22 | semidirect |
| 21. C2×D8×C199 | C22 | semidirect |
| 23. #108×C199 | C22 | semidirect |
| 93. C199 | #2192 | semidirect |
| 98. #472 | D199 | semidirect |
| 110. C2×D8 | C2×D199 | semidirect |
| 117. #108 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164823 | 2 |
| #27164454 | 2 |
| C2×#20263896 | 2 |
| #27163830 | 2 |
| #27163824 | 2 |
| #27163802 | 2 |
| #472×C199 | 2 |
| #2192 | 199 |