Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
202 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 60 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. C2×D349⋊C8 | C2 | semidirect |
| 2. C2×C4⋊#13063703 | C2 | semidirect |
| 3. #26013701 | C2 | direct (N × H) |
| 7. D349⋊C8 | C22 | semidirect |
| 10. C4⋊#13063703 | C22 | semidirect |
| 12. C2×D1396 | C4 | semidirect |
| 16. D4×D349 | C4 | semidirect |
| 19. C2×D4×C349 | C4 | semidirect |
| 30. D1396 | C2×C4 | semidirect |
| 40. D4×C349 | C2×C4 | semidirect |
| 60. C2×C349 | #102 | semidirect |
| 63. D349 | #102 | semidirect |
| 66. C349 | C2×#102 | semidirect |
| 79. C2×D4 | #13063703 | semidirect |
| 99. D4 | C2×#13063703 | semidirect |
| 131. C2 | #26013701 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D349⋊C8 | 2 |
| C2×C4⋊#13063703 | 2 |
| #26013701 | 2 |
| C2×D4×D349 | 2 |
| C2×#102 | 349 |