Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
150 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 4. #26013564 | C2 | semidirect |
| 5. #26013563 | C2 | semidirect |
| 6. #26013562 | C2 | semidirect |
| 7. #103×C349 | C2 | semidirect |
| 11. Q8×D349 | C4 | semidirect |
| 54. C349 | #419 | semidirect |
| 62. #103 | D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D349 | 2 |
| C2×#19150216 | 2 |
| #26013597 | 2 |
| #26013564 | 2 |
| #26013563 | 2 |
| #26013562 | 2 |
| #103×C349 | 2 |
| #419 | 349 |