Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
336 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 77. Dic346 | Q16 | semidirect |
| 112. C173 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic346 | 2 |
| #26012219 | 2 |
| #26011842 | 2 |
| #26011840 | 2 |
| #26011786 | 2 |
| #26011785 | 2 |
| #26011701 | 2 |
| #26011699 | 2 |
| C8×Dic346 | 2 |
| #26011583 | 2 |
| C4×Q16×C173 | 2 |
| #3363 | 173 |