Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 394 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×#20263988 | C2 | semidirect |
| 3. C2×#20263942 | C2 | semidirect |
| 4. C2×#20263881 | C2 | semidirect |
| 5. #27164028 | C2 | semidirect |
| 6. #27163779 | C2 | semidirect |
| 7. C2×#100×C199 | C2 | semidirect |
| 39. C2×Dic398 | D4 | semidirect |
| 54. C4×Dic199 | D4 | semidirect |
| 66. M16×C199 | D4 | semidirect |
| 131. C199 | #2004 | semidirect |
| 138. C2×#100 | D199 | semidirect |
| 191. M16 | C22⋊D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263988 | 2 |
| #27164585 | 2 |
| C2×#20263942 | 2 |
| C2×#20263881 | 2 |
| #27164028 | 2 |
| #27163779 | 2 |
| C2×#100×C199 | 2 |
| #2004 | 199 |