Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20259370 | C2 | semidirect |
| 2. #20259354 | C2 | semidirect |
| 3. #20259353 | C2 | semidirect |
| 4. #20259345 | C2 | semidirect |
| 5. #20259344 | C2 | semidirect |
| 6. Q16×D191 | C2 | semidirect |
| 7. #20259328 | C2 | semidirect |
| 8. C2×Q16×C191 | C2 | semidirect |
| 59. C191 | #578 | semidirect |
| 67. C2×Q16 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259370 | 2 |
| #20259354 | 2 |
| #20259353 | 2 |
| #20259345 | 2 |
| #20259344 | 2 |
| Q16×D191 | 2 |
| #20259328 | 2 |
| C2×Q16×C191 | 2 |
| #578 | 191 |