Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×#19149618 | C2 | semidirect |
| 3. #26011309 | C2 | semidirect |
| 4. C22⋊#14583801 | C2 | semidirect |
| 5. #26011270 | C2 | semidirect |
| 6. C16×Dic173 | C2 | semidirect |
| 7. C2×M32×C173 | C2 | semidirect |
| 39. C16×C173 | D4 | semidirect |
| 69. Dic173 | M32 | semidirect |
| 75. C173 | #2169 | semidirect |
| 78. C2×M32 | D173 | semidirect |
| 115. C16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19149618 | 2 |
| C8×C22⋊D173 | 2 |
| #26011309 | 2 |
| C22⋊#14583801 | 2 |
| #26011270 | 2 |
| C16×Dic173 | 2 |
| C2×M32×C173 | 2 |
| #2169 | 173 |