Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
484 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 206 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. #26012498 | C2 | semidirect |
| 3. #26012495 | C2 | semidirect |
| 4. D173⋊(C4⋊C8) | C2 | semidirect |
| 59. C4×C173 | #131 | semidirect |
| 68. C173 | #2906 | semidirect |
| 132. C4 | #19149767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149767 | 2 |
| #26012498 | 2 |
| #26012495 | 2 |
| D173⋊(C4⋊C8) | 2 |
| C4×#14583827 | 2 |
| #2906 | 173 |