Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 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. #26012289 | C2 | semidirect |
| 2. #26012058 | C2 | semidirect |
| 3. #26011507 | C2 | semidirect |
| 4. #26011496 | C2 | semidirect |
| 5. #26011465 | C2 | semidirect |
| 6. #26011263 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8)×C173 | C2 | semidirect |
| 46. C2×#13063436 | D4 | semidirect |
| 59. C2×Q8×C173 | D4 | semidirect |
| 67. C2×D4×C173 | D4 | semidirect |
| 73. M16×C173 | D4 | semidirect |
| 142. C173 | #2008 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D173 | semidirect |
| 184. C2×Q8 | C22⋊D173 | semidirect |
| 195. C2×D4 | C22⋊D173 | semidirect |
| 208. M16 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012289 | 2 |
| #26012058 | 2 |
| #26011507 | 2 |
| #26011496 | 2 |
| #26011465 | 2 |
| #26011263 | 2 |
| C2×AGL(1,ℤ/8)×C173 | 2 |
| #2008 | 173 |