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 |
|---|---|---|
| 4. #27163771 | C2 | semidirect |
| 5. #27163767 | C2 | semidirect |
| 6. #27163764 | C2 | semidirect |
| 7. #498×C199 | C2 | semidirect |
| 59. C8×C199 | SD16 | semidirect |
| 76. C199 | #1691 | semidirect |
| 78. #498 | D199 | semidirect |
| 136. C8 | #15691873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164305 | 2 |
| #27164220 | 2 |
| #27164097 | 2 |
| #27163771 | 2 |
| #27163767 | 2 |
| #27163764 | 2 |
| #498×C199 | 2 |
| #1691 | 199 |