Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 3. #27164028 | C2 | semidirect |
| 4. #27164026 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 7. H(3,ℤ/4)×C199 | C2 | semidirect |
| 14. #20263955 | C4 | semidirect |
| 15. #20263943 | C4 | semidirect |
| 109. C199 | #1909 | semidirect |
| 117. H(3,ℤ/4) | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164784 | 2 |
| #27164594 | 2 |
| #27164028 | 2 |
| #27164026 | 2 |
| #27163991 | 2 |
| #27163774 | 2 |
| H(3,ℤ/4)×C199 | 2 |
| #1909 | 199 |