Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20263374 | C2 | semidirect |
| 2. #20263373 | C2 | semidirect |
| 3. #20263359 | C2 | semidirect |
| 4. #20263358 | C2 | semidirect |
| 5. #20263355 | C2 | semidirect |
| 6. #20263347 | C2 | semidirect |
| 7. #20263346 | C2 | semidirect |
| 8. C2×#15691348 | C2 | semidirect |
| 9. Q16×D197 | C2 | semidirect |
| 10. #20263334 | C2 | semidirect |
| 11. #137×C197 | C2 | semidirect |
| 87. C197 | #578 | semidirect |
| 94. #137 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20263374 | 2 |
| #20263373 | 2 |
| #20263359 | 2 |
| #20263358 | 2 |
| #20263355 | 2 |
| #20263347 | 2 |
| #20263346 | 2 |
| C2×#15691348 | 2 |
| Q16×D197 | 2 |
| #20263334 | 2 |
| #137×C197 | 2 |
| #578 | 197 |