Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 54 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. D173⋊#101 | C2 | semidirect |
| 2. #26012400 | C2 | semidirect |
| 3. #26012399 | C2 | semidirect |
| 7. #19149740 | C22 | semidirect |
| 86. D173 | #355 | semidirect |
| 87. C173 | C2×#355 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D173⋊#101 | 2 |
| #26012400 | 2 |
| #26012399 | 2 |
| #124×D173 | 2 |
| C2×#355 | 173 |