Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
348 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 2. #26011620 | C2 | semidirect |
| 3. #26011618 | C2 | semidirect |
| 33. C2×#13063436 | Q8 | semidirect |
| 83. C173 | #2961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| #26011620 | 2 |
| #26011618 | 2 |
| #26011517 | 2 |
| #26011514 | 2 |
| #26011449 | 2 |
| #26011447 | 2 |
| C2×#19149589 | 2 |
| #424×C173 | 2 |
| #2961 | 173 |