Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
578 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 97 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. #27164493 | C2 | semidirect |
| 2. C2×#20263870 | C2 | semidirect |
| 3. #27163874 | C2 | semidirect |
| 4. #27163784 | C2 | semidirect |
| 17. #120×C199 | C4 | semidirect |
| 22. C22×Dic199 | D4 | semidirect |
| 36. C24×C199 | C2×C4 | semidirect |
| 49. C22⋊C4×C199 | C2×C4 | semidirect |
| 71. C23×C199 | C22⋊C4 | semidirect |
| 84. C2×C4×C199 | C22⋊C4 | semidirect |
| 119. C199 | #1889 | semidirect |
| 130. #120 | Dic199 | semidirect |
| 145. C24 | C2×Dic199 | semidirect |
| 168. C22⋊C4 | C2×Dic199 | semidirect |
| 186. C23 | C22⋊Dic199 | semidirect |
| 204. C2×C4 | C22⋊Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164493 | 2 |
| C2×#20263870 | 2 |
| #27163874 | 2 |
| #27163784 | 2 |
| C2×#120×C199 | 2 |
| #1889 | 199 |