Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 478 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 |
|---|---|---|
| 1. C2×#20263351 | C2 | semidirect |
| 2. #27161643 | C2 | semidirect |
| 3. C2×#20263323 | C2 | semidirect |
| 4. #27161085 | C2 | semidirect |
| 5. C2×#20263242 | C2 | semidirect |
| 6. #27160839 | C2 | semidirect |
| 7. C2×#104×C197 | C2 | semidirect |
| 44. C2×D788 | D4 | semidirect |
| 49. #15691342 | D4 | semidirect |
| 51. C4⋊Dic197 | D4 | semidirect |
| 59. C2×Q8×C197 | D4 | semidirect |
| 61. C2×D4×C197 | D4 | semidirect |
| 69. C42×C197 | D4 | semidirect |
| 138. C197 | #2002 | semidirect |
| 143. C2×#104 | D197 | semidirect |
| 174. C2×Q8 | D788 | semidirect |
| 191. C2×D4 | D788 | semidirect |
| 208. C42 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| #27161643 | 2 |
| C2×#20263323 | 2 |
| #27161085 | 2 |
| C2×#20263242 | 2 |
| #27160839 | 2 |
| C2×#104×C197 | 2 |
| #2002 | 197 |