Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
310 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 93 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. #27164496 | C2 | semidirect |
| 3. #27164027 | C2 | semidirect |
| 5. #27163789 | C2 | semidirect |
| 6. #27163775 | C2 | semidirect |
| 22. C2×Q16×C199 | C4 | semidirect |
| 23. C2×SD16×C199 | C4 | semidirect |
| 109. C199 | #1905 | semidirect |
| 122. C2×Q16 | Dic199 | semidirect |
| 123. C2×SD16 | Dic199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164496 | 2 |
| #27164035 | 2 |
| #27164027 | 2 |
| #27163992 | 2 |
| #27163789 | 2 |
| #27163775 | 2 |
| C2×#137×C199 | 2 |
| #1905 | 199 |