Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×D349 | C2 | semidirect |
| 3. C2×#19150210 | C2 | semidirect |
| 4. C2×#19150210 | C2 | semidirect |
| 5. C2×#19150210 | C2 | semidirect |
| 6. #26013546 | C2 | semidirect |
| 7. #95×C349 | C2 | semidirect |
| 12. C2×D1396 | C4 | semidirect |
| 35. C22×D349 | C2×C4 | semidirect |
| 44. C2×Dic349 | D4 | semidirect |
| 54. C2×C4×C349 | C2×C4 | semidirect |
| 55. C2×C4×C349 | D4 | semidirect |
| 76. C2×D349 | C22⋊C4 | semidirect |
| 91. C349 | #386 | semidirect |
| 99. #95 | D349 | semidirect |
| 146. C2×C4 | C4×D349 | semidirect |
| 147. C2×C4 | D1396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1396 | 2 |
| C22×C4×D349 | 2 |
| C2×#19150210 | 2 |
| #26013546 | 2 |
| #95×C349 | 2 |
| #386 | 349 |