Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
170 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 1. D349⋊M16 | C2 | semidirect |
| 2. C2×C4×#13063703 | C2 | semidirect |
| 3. #26013704 | C2 | semidirect |
| 4. #26013703 | C2 | semidirect |
| 7. #19150243 | C22 | semidirect |
| 11. C4×#13063703 | C22 | semidirect |
| 14. #19150233 | C4 | semidirect |
| 17. Q8×D349 | C4 | semidirect |
| 19. D4×D349 | C4 | semidirect |
| 22. #41×C349 | C4 | semidirect |
| 29. Dic698 | C2×C4 | semidirect |
| 31. D1396 | C2×C4 | semidirect |
| 44. Q8×C349 | C2×C4 | semidirect |
| 46. D4×C349 | C2×C4 | semidirect |
| 68. D349 | #104 | semidirect |
| 69. C349 | C2×#104 | semidirect |
| 81. #41 | #13063703 | semidirect |
| 97. Q8 | C2×#13063703 | semidirect |
| 104. D4 | C2×#13063703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D349⋊M16 | 2 |
| C2×C4×#13063703 | 2 |
| #26013704 | 2 |
| #26013703 | 2 |
| #41×D349 | 2 |
| C2×#104 | 349 |