Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 1. C2×C8×D349 | C2 | semidirect |
| 3. #26013568 | C2 | semidirect |
| 4. C22⋊#14584095 | C2 | semidirect |
| 5. #26013551 | C2 | semidirect |
| 6. C8×Dic349 | C2 | semidirect |
| 7. C22×C8×C349 | C2 | semidirect |
| 22. C22⋊D349 | C8 | direct (N × H) |
| 36. C8×C349 | D4 | semidirect |
| 39. C22×C349 | C2×C8 | semidirect |
| 43. C2×D349 | C2×C8 | semidirect |
| 49. Dic349 | C2×C8 | semidirect |
| 55. C349 | C8×D4 | semidirect |
| 58. C22×C8 | D349 | semidirect |
| 92. C8 | C22⋊D349 | direct (N × H) |
| 98. C22 | C8×D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D349 | 2 |
| C4×C22⋊D349 | 2 |
| #26013568 | 2 |
| C22⋊#14584095 | 2 |
| #26013551 | 2 |
| C8×Dic349 | 2 |
| C22×C8×C349 | 2 |
| C8×D4 | 349 |