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. #20259369 | C2 | semidirect |
| 3. #20259355 | C2 | semidirect |
| 4. #20259354 | C2 | semidirect |
| 5. #20259351 | C2 | semidirect |
| 6. #20259343 | C2 | semidirect |
| 7. #20259342 | C2 | semidirect |
| 8. C2×#15690277 | C2 | semidirect |
| 9. Q16×D191 | C2 | semidirect |
| 10. #20259330 | C2 | semidirect |
| 11. #137×C191 | C2 | semidirect |
| 87. C191 | #578 | semidirect |
| 94. #137 | D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20259370 | 2 |
| #20259369 | 2 |
| #20259355 | 2 |
| #20259354 | 2 |
| #20259351 | 2 |
| #20259343 | 2 |
| #20259342 | 2 |
| C2×#15690277 | 2 |
| Q16×D191 | 2 |
| #20259330 | 2 |
| #137×C191 | 2 |
| #578 | 191 |