Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. #27164066 | C2 | semidirect |
| 5. #27163790 | C2 | semidirect |
| 6. #27163778 | C2 | semidirect |
| 7. C4×M16×C199 | C2 | semidirect |
| 16. #20263873 | C4 | semidirect |
| 17. #20263871 | C4 | semidirect |
| 95. C199 | #1932 | semidirect |
| 101. C4×M16 | D199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164066 | 2 |
| #27164034 | 2 |
| C2×#20263883 | 2 |
| #27164000 | 2 |
| #27163790 | 2 |
| #27163778 | 2 |
| C4×M16×C199 | 2 |
| #1932 | 199 |