Finite Group DatabasebetaFinite Group DatabasebetaOrder 22336.
114 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 114 conjugacy classes of subgroups — too many to draw. Only its 45 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×#19150223 | C2 | semidirect |
| 4. #26013572 | C2 | semidirect |
| 5. #26013563 | C2 | semidirect |
| 6. #26013562 | C2 | semidirect |
| 38. C22×C349 | Q16 | semidirect |
| 51. C349 | #467 | semidirect |
| 90. C22 | #19150223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150223 | 2 |
| C22×#14584095 | 2 |
| #26013618 | 2 |
| #26013572 | 2 |
| #26013563 | 2 |
| #26013562 | 2 |
| C22⋊Q8×C349 | 2 |
| #467 | 349 |