Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
210 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 210 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. C22⋊C4×D349 | C2 | semidirect |
| 3. #26013554 | C2 | semidirect |
| 4. #26013553 | C2 | semidirect |
| 5. #99×C349 | C2 | semidirect |
| 6. C23×D349 | C4 | semidirect |
| 8. C2×D1396 | C4 | semidirect |
| 9. C2×C22⋊D349 | C4 | semidirect |
| 14. C2×C4×D349 | C4 | semidirect |
| 15. C22⋊Dic349 | C22 | semidirect |
| 18. C22⋊C4×C349 | C22 | semidirect |
| 25. C22×D349 | C2×C4 | semidirect |
| 32. C2×Dic349 | C2×C4 | semidirect |
| 36. C23×C349 | C2×C4 | semidirect |
| 40. C2×C4×C349 | C2×C4 | semidirect |
| 68. D349 | #99 | direct (N × H) |
| 69. C349 | C2×#99 | semidirect |
| 75. #99 | D349 | direct (N × H) |
| 88. C22⋊C4 | C2×D349 | semidirect |
| 98. C23 | C4×D349 | semidirect |
| 110. C2×C4 | C4×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 |
| C22⋊C4×D349 | 2 |
| #26013554 | 2 |
| #26013553 | 2 |
| #99×C349 | 2 |
| C2×#99 | 349 |