Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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×#19150220 | C2 | semidirect |
| 3. Q8×Dic349 | C2 | semidirect |
| 4. #26013568 | C2 | semidirect |
| 5. #26013561 | C2 | semidirect |
| 6. #26013560 | C2 | semidirect |
| 7. C2×SD16×C349 | C2 | semidirect |
| 32. Q8×C349 | D4 | semidirect |
| 50. Dic349 | SD16 | semidirect |
| 56. C349 | #460 | semidirect |
| 59. C2×SD16 | D349 | semidirect |
| 81. Q8 | C22⋊D349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150220 | 2 |
| #26013635 | 2 |
| Q8×Dic349 | 2 |
| #26013568 | 2 |
| #26013561 | 2 |
| #26013560 | 2 |
| C2×SD16×C349 | 2 |
| #460 | 349 |