Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
108 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 35 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. #20259350 | C2 | semidirect |
| 2. #20259348 | C2 | semidirect |
| 3. C2×#15690272 | C2 | semidirect |
| 4. #20259330 | C2 | semidirect |
| 5. #20259257 | C2 | semidirect |
| 6. #20259238 | C2 | semidirect |
| 7. #100×C191 | C2 | semidirect |
| 53. C191 | #472 | semidirect |
| 61. #100 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259350 | 2 |
| #20259348 | 2 |
| C2×#15690272 | 2 |
| #20259330 | 2 |
| #20259257 | 2 |
| #20259238 | 2 |
| #100×C191 | 2 |
| #472 | 191 |