Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26011974 | C2 | semidirect |
| 2. C2×#19149606 | C2 | semidirect |
| 3. #26011496 | C2 | semidirect |
| 4. #26011394 | C2 | semidirect |
| 5. #26011259 | C2 | semidirect |
| 6. #26011252 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C173 | C4 | semidirect |
| 58. C2×D4×C173 | C2×C4 | semidirect |
| 65. M16×C173 | C2×C4 | semidirect |
| 84. Q8×C173 | C22⋊C4 | semidirect |
| 92. D4×C173 | C22⋊C4 | semidirect |
| 132. C173 | #1883 | semidirect |
| 144. AGL(1,ℤ/8) | Dic173 | semidirect |
| 173. C2×D4 | C2×Dic173 | semidirect |
| 185. M16 | C2×Dic173 | semidirect |
| 208. Q8 | C22⋊Dic173 | semidirect |
| 216. D4 | C22⋊Dic173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011974 | 2 |
| C2×#19149606 | 2 |
| #26011496 | 2 |
| #26011394 | 2 |
| #26011259 | 2 |
| #26011252 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #1883 | 173 |