Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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. M16×D349 | C2 | semidirect |
| 3. #26013556 | C2 | semidirect |
| 4. #26013555 | C2 | semidirect |
| 5. #100×C349 | C2 | semidirect |
| 12. #19150217 | C22 | semidirect |
| 16. M16×C349 | C22 | semidirect |
| 49. D349 | #100 | direct (N × H) |
| 50. C349 | C2×#100 | semidirect |
| 56. #100 | D349 | direct (N × H) |
| 66. M16 | C2×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D349 | 2 |
| M16×D349 | 2 |
| #26013556 | 2 |
| #26013555 | 2 |
| #100×C349 | 2 |
| C2×#100 | 349 |