Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 3. #26011800 | C2 | semidirect |
| 4. #26011796 | C2 | semidirect |
| 5. #26011784 | C2 | semidirect |
| 6. #26011774 | C2 | semidirect |
| 72. C2×Q8×C173 | Q8 | semidirect |
| 129. C173 | #3078 | semidirect |
| 177. C2×Q8 | Dic346 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012044 | 2 |
| C2×Q8×Dic173 | 2 |
| #26011800 | 2 |
| #26011796 | 2 |
| #26011784 | 2 |
| #26011774 | 2 |
| #26011534 | 2 |
| #26011533 | 2 |
| #26011514 | 2 |
| #26011500 | 2 |
| #419×C173 | 2 |
| #3078 | 173 |