Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 2. #20259330 | C2 | semidirect |
| 3. #20259329 | C2 | semidirect |
| 4. #20259328 | C2 | semidirect |
| 5. C2×#15690270 | C2 | semidirect |
| 6. M16×D191 | C2 | semidirect |
| 7. #131×C191 | C2 | semidirect |
| 14. #15690271 | C22 | semidirect |
| 17. #15690270 | C22 | semidirect |
| 18. #15690270 | C22 | semidirect |
| 19. C2×C191⋊C8 | C22 | semidirect |
| 20. C8×D191 | C22 | semidirect |
| 22. M16×C191 | C22 | semidirect |
| 23. C2×C8×C191 | C22 | semidirect |
| 52. C191 | #568 | semidirect |
| 58. #131 | D191 | semidirect |
| 73. M16 | C2×D191 | semidirect |
| 76. C2×C8 | C2×D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D191 | 2 |
| #20259330 | 2 |
| #20259329 | 2 |
| #20259328 | 2 |
| C2×#15690270 | 2 |
| M16×D191 | 2 |
| #131×C191 | 2 |
| #568 | 191 |