Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27161425 | C2 | semidirect |
| 2. #27161284 | C2 | semidirect |
| 3. D4×#13096802 | C2 | semidirect |
| 4. #27160831 | C2 | semidirect |
| 5. #27160826 | C2 | semidirect |
| 6. #27160823 | C2 | semidirect |
| 84. C197 | #1681 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161425 | 2 |
| #27161284 | 2 |
| D4×#13096802 | 2 |
| #27160831 | 2 |
| #27160826 | 2 |
| #27160823 | 2 |
| #459×C197 | 2 |
| #1681 | 197 |