Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
114 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 39 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. C4⋊C4×D191 | C2 | semidirect |
| 3. #20259255 | C2 | semidirect |
| 4. #20259244 | C2 | semidirect |
| 5. #20259242 | C2 | semidirect |
| 6. (C2×D191)⋊C8 | C2 | semidirect |
| 7. #107×C191 | C2 | semidirect |
| 52. C191 | #480 | semidirect |
| 57. #107 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259297 | 2 |
| C4⋊C4×D191 | 2 |
| #20259255 | 2 |
| #20259244 | 2 |
| #20259242 | 2 |
| (C2×D191)⋊C8 | 2 |
| #107×C191 | 2 |
| #480 | 191 |