Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
262 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 73 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. #27163779 | C2 | semidirect |
| 5. #27163777 | C2 | semidirect |
| 6. #27163774 | C2 | semidirect |
| 7. H(3,ℤ/4)×C199 | C2 | semidirect |
| 14. #20263912 | C4 | semidirect |
| 16. C42×D199 | C4 | semidirect |
| 102. C199 | #1827 | semidirect |
| 110. 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 |
|---|---|
| #27164486 | 2 |
| #27164000 | 2 |
| #27163991 | 2 |
| #27163779 | 2 |
| #27163777 | 2 |
| #27163774 | 2 |
| H(3,ℤ/4)×C199 | 2 |
| #1827 | 199 |