Finite Group DatabasebetaFinite Group DatabasebetaOrder 12608.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#15691358 | C2 | semidirect |
| 2. #20263357 | C2 | semidirect |
| 3. #20263356 | C2 | semidirect |
| 4. #20263352 | C2 | semidirect |
| 5. #20263351 | C2 | semidirect |
| 6. #20263346 | C2 | semidirect |
| 7. C2×#15691342 | C2 | semidirect |
| 8. C2×#41×C197 | C2 | semidirect |
| 12. #15691358 | C22 | semidirect |
| 13. C2×Dic394 | C22 | semidirect |
| 14. C2×D788 | C22 | semidirect |
| 17. #15691348 | C22 | semidirect |
| 18. #15691346 | C22 | semidirect |
| 19. #15691345 | C22 | semidirect |
| 20. #15691343 | C22 | semidirect |
| 21. #15691342 | C22 | semidirect |
| 22. #15691342 | C22 | semidirect |
| 23. C2×#13096802 | C22 | semidirect |
| 27. #41×C197 | C22 | semidirect |
| 28. C2×Q8×C197 | C22 | semidirect |
| 30. C2×D4×C197 | C22 | semidirect |
| 81. C197 | #575 | semidirect |
| 84. C2×#41 | D197 | semidirect |
| 98. #41 | C2×D197 | semidirect |
| 100. C2×Q8 | C2×D197 | semidirect |
| 104. C2×D4 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15691358 | 2 |
| #20263357 | 2 |
| #20263356 | 2 |
| #20263352 | 2 |
| #20263351 | 2 |
| #20263346 | 2 |
| C2×#15691342 | 2 |
| C2×#41×C197 | 2 |
| #575 | 197 |