Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
250 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27161364 | C2 | semidirect |
| 3. #27161284 | C2 | semidirect |
| 4. #27160823 | C2 | semidirect |
| 5. Q8⋊#13096802 | C2 | semidirect |
| 6. D4⋊#13096802 | C2 | semidirect |
| 59. Q8×C197 | SD16 | semidirect |
| 99. C197 | #1642 | semidirect |
| 155. Q8 | #15691346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161425 | 2 |
| #27161364 | 2 |
| #27161284 | 2 |
| #27160823 | 2 |
| Q8⋊#13096802 | 2 |
| D4⋊#13096802 | 2 |
| #550×C197 | 2 |
| #1642 | 197 |