Finite Group DatabasebetaFinite Group DatabasebetaOrder 25472.
308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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. #27164364 | C2 | semidirect |
| 2. #27164298 | C2 | semidirect |
| 3. #27164223 | C2 | semidirect |
| 4. #27163762 | C2 | semidirect |
| 5. D4⋊(C199⋊C8) | C2 | semidirect |
| 6. D4⋊(C199⋊C8) | C2 | semidirect |
| 9. #20263955 | C22 | semidirect |
| 11. C4⋊(C199⋊C8) | C22 | semidirect |
| 12. C4⋊(C199⋊C8) | C22 | semidirect |
| 16. C4×C199⋊C8 | C22 | semidirect |
| 74. D4×C199 | SD16 | semidirect |
| 109. C199 | #1639 | semidirect |
| 180. D4 | #15691874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27164364 | 2 |
| #27164298 | 2 |
| #27164223 | 2 |
| #27163762 | 2 |
| D4⋊(C199⋊C8) | 2 |
| D42×C199 | 2 |
| #1639 | 199 |