Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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. #27164416 | C2 | semidirect |
| 3. #27164303 | C2 | semidirect |
| 5. #27163763 | C2 | semidirect |
| 7. Q8⋊C8×C199 | C2 | semidirect |
| 66. Q8×C199 | SD16 | semidirect |
| 92. C199 | #1651 | semidirect |
| 99. Q8⋊C8 | D199 | semidirect |
| 150. Q8 | #15691875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D796 | 2 |
| #27164416 | 2 |
| #27164303 | 2 |
| #27164224 | 2 |
| #27163763 | 2 |
| #27163747 | 2 |
| Q8⋊C8×C199 | 2 |
| #1651 | 199 |