Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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. #26012543 | C2 | semidirect |
| 2. #26012542 | C2 | semidirect |
| 3. Q8×#13063443 | C2 | semidirect |
| 31. #14583836 | Q8 | semidirect |
| 90. C173 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012543 | 2 |
| #26012542 | 2 |
| Q8×#13063443 | 2 |
| #26012498 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #26012456 | 2 |
| C4×#14583836 | 2 |
| #26012046 | 2 |
| #2962 | 173 |