Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
320 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 320 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. #27161229 | C2 | semidirect |
| 2. #27161212 | C2 | semidirect |
| 3. #27160988 | C2 | semidirect |
| 4. #27160816 | C2 | semidirect |
| 5. #27160813 | C2 | semidirect |
| 6. #27160803 | C2 | semidirect |
| 7. #538×C197 | C2 | semidirect |
| 41. C2×Q8×C197 | D4 | semidirect |
| 45. C2×D4×C197 | D4 | semidirect |
| 51. C4⋊C4×C197 | D4 | semidirect |
| 52. C4⋊C4×C197 | D4 | semidirect |
| 135. C197 | #1600 | semidirect |
| 137. #538 | D197 | semidirect |
| 165. C2×Q8 | C22⋊D197 | semidirect |
| 175. C2×D4 | C22⋊D197 | semidirect |
| 186. C4⋊C4 | C22⋊D197 | semidirect |
| 187. C4⋊C4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161229 | 2 |
| #27161212 | 2 |
| #27160988 | 2 |
| #27160816 | 2 |
| #27160813 | 2 |
| #27160803 | 2 |
| #538×C197 | 2 |
| #1600 | 197 |