Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
266 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 151 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 | direct (N × H) |
| 3. C2×#15690270 | C2 | semidirect |
| 4. C22×C191⋊C8 | C2 | semidirect |
| 5. C2×C8×D191 | C2 | semidirect |
| 6. C2×M16×C191 | C2 | semidirect |
| 13. #15690270 | C22 | semidirect |
| 16. C2×C191⋊C8 | C22 | semidirect |
| 17. C8×D191 | C22 | semidirect |
| 19. M16×C191 | C22 | semidirect |
| 46. C2×C191 | #131 | semidirect |
| 49. C191 | C2×#131 | semidirect |
| 54. C2×M16 | D191 | semidirect |
| 65. M16 | C2×D191 | semidirect |
| 97. C2 | #20259330 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690287 | 2 |
| #20259330 | 2 |
| C2×#15690270 | 2 |
| C22×C191⋊C8 | 2 |
| C2×C8×D191 | 2 |
| C2×M16×C191 | 2 |
| C2×#131 | 191 |