Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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. #27164391 | C2 | semidirect |
| 2. #27164298 | C2 | semidirect |
| 4. #27163769 | C2 | semidirect |
| 5. #27163765 | C2 | semidirect |
| 6. #27163761 | C2 | semidirect |
| 7. C8×D4×C199 | C2 | semidirect |
| 56. D4×C199 | SD16 | semidirect |
| 65. C8×C199 | D8 | semidirect |
| 85. C199 | #1665 | semidirect |
| 90. C8×D4 | D199 | semidirect |
| 139. D4 | #15691875 | semidirect |
| 151. C8 | #15691871 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164391 | 2 |
| #27164298 | 2 |
| #27164213 | 2 |
| #27163769 | 2 |
| #27163765 | 2 |
| #27163761 | 2 |
| C8×D4×C199 | 2 |
| #1665 | 199 |