Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
248 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 4. #27163750 | C2 | semidirect |
| 5. Q8⋊(C199⋊C8) | C2 | semidirect |
| 6. #27163748 | C2 | semidirect |
| 7. Q8⋊C8×C199 | C2 | semidirect |
| 60. Dic398 | M16 | semidirect |
| 76. Q8×C199 | M16 | semidirect |
| 104. C199 | #1487 | semidirect |
| 112. Q8⋊C8 | D199 | semidirect |
| 167. Q8 | #15691869 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D199 | 2 |
| #27164069 | 2 |
| #27164040 | 2 |
| #27163750 | 2 |
| Q8⋊(C199⋊C8) | 2 |
| #27163748 | 2 |
| Q8⋊C8×C199 | 2 |
| #1487 | 199 |