Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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×#19150217 | C2 | semidirect |
| 3. #26013567 | C2 | direct (N × H) |
| 4. C2×C42×C349 | C2 | semidirect |
| 7. #19150233 | C4 | semidirect |
| 9. C2×Dic698 | C4 | semidirect |
| 10. C2×D1396 | C4 | semidirect |
| 14. #19150217 | C22 | semidirect |
| 19. C42×C349 | C22 | semidirect |
| 22. Dic698 | C2×C4 | semidirect |
| 24. D1396 | C2×C4 | semidirect |
| 54. C2×C349 | #104 | semidirect |
| 57. C349 | C2×#104 | semidirect |
| 61. C2×C42 | D349 | semidirect |
| 77. C42 | C2×D349 | semidirect |
| 113. C2 | #26013567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150233 | 2 |
| C2×#19150217 | 2 |
| #26013567 | 2 |
| C2×C42×C349 | 2 |
| C2×#104 | 349 |