Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×#19150223 | C2 | semidirect |
| 4. #26013564 | C2 | semidirect |
| 5. #26013563 | C2 | semidirect |
| 7. C2×Q16×C349 | C2 | semidirect |
| 45. C2×D349 | Q16 | semidirect |
| 57. C349 | #451 | semidirect |
| 61. C2×Q16 | 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×#19150223 | 2 |
| #26013615 | 2 |
| #26013564 | 2 |
| #26013563 | 2 |
| #26013551 | 2 |
| C2×Q16×C349 | 2 |
| #451 | 349 |