Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#20263357 | C2 | semidirect |
| 3. C2×#20263254 | C2 | semidirect |
| 4. #27161088 | C2 | semidirect |
| 5. C2×#20263243 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. C2×#124×C197 | C2 | semidirect |
| 43. #15691342 | D4 | semidirect |
| 56. C2×Q8×C197 | D4 | semidirect |
| 68. C42×C197 | D4 | semidirect |
| 131. C197 | #2004 | semidirect |
| 135. C2×#124 | D197 | semidirect |
| 172. C2×Q8 | C22⋊D197 | semidirect |
| 200. C42 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263357 | 2 |
| #27161646 | 2 |
| C2×#20263254 | 2 |
| #27161088 | 2 |
| C2×#20263243 | 2 |
| #27160839 | 2 |
| C2×#124×C197 | 2 |
| #2004 | 197 |