Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #27164391 | C2 | semidirect |
| 3. #27164313 | C2 | semidirect |
| 4. #27164309 | C2 | semidirect |
| 5. #27163761 | C2 | semidirect |
| 6. #27163747 | C2 | semidirect |
| 7. Q8⋊C8×C199 | C2 | semidirect |
| 69. Q8×C199 | SD16 | semidirect |
| 98. C199 | #1631 | semidirect |
| 105. Q8⋊C8 | D199 | semidirect |
| 153. Q8 | #15691875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164690 | 2 |
| #27164391 | 2 |
| #27164313 | 2 |
| #27164309 | 2 |
| #27163761 | 2 |
| #27163747 | 2 |
| Q8⋊C8×C199 | 2 |
| #1631 | 199 |