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. #27164456 | C2 | semidirect |
| 3. C2×D3184 | C2 | semidirect |
| 4. #27164288 | C2 | semidirect |
| 5. #27163832 | C2 | semidirect |
| 6. #27163826 | C2 | semidirect |
| 7. #350×C199 | C2 | semidirect |
| 16. C2×D1592 | C22 | semidirect |
| 20. #20263891 | C22 | semidirect |
| 23. M32×C199 | C22 | semidirect |
| 24. C2×C16×C199 | C22 | semidirect |
| 93. C199 | #2192 | semidirect |
| 101. #350 | D199 | semidirect |
| 115. M32 | C2×D199 | semidirect |
| 116. C2×C16 | C2×D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164823 | 2 |
| #27164456 | 2 |
| C2×D3184 | 2 |
| #27164288 | 2 |
| #27163832 | 2 |
| #27163826 | 2 |
| #350×C199 | 2 |
| #2192 | 199 |