Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 55 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. #27164416 | C2 | semidirect |
| 5. #27163766 | C2 | semidirect |
| 6. #27163765 | C2 | semidirect |
| 7. #335×C199 | C2 | semidirect |
| 59. C8×C199 | SD16 | semidirect |
| 76. C199 | #1691 | semidirect |
| 82. #335 | D199 | semidirect |
| 136. C8 | #15691875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164416 | 2 |
| #27164309 | 2 |
| #27164224 | 2 |
| #27164097 | 2 |
| #27163766 | 2 |
| #27163765 | 2 |
| #335×C199 | 2 |
| #1691 | 199 |