Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
382 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27164594 | C2 | semidirect |
| 3. C2×#20263942 | C2 | semidirect |
| 4. C2×#20263881 | C2 | semidirect |
| 5. C2×#20263873 | C2 | semidirect |
| 6. #27163777 | C2 | semidirect |
| 7. #418×C199 | C2 | semidirect |
| 130. C199 | #2003 | semidirect |
| 136. #418 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263981 | 2 |
| #27164594 | 2 |
| C2×#20263942 | 2 |
| C2×#20263881 | 2 |
| C2×#20263873 | 2 |
| #27163777 | 2 |
| #418×C199 | 2 |
| #2003 | 199 |