Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
496 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#14583811 | C2 | semidirect |
| 2. C2×#19149653 | C2 | semidirect |
| 3. C2×#19149600 | C2 | semidirect |
| 4. C2×#19149599 | C2 | semidirect |
| 5. C2×C22⋊#13063436 | C2 | semidirect |
| 6. #26011253 | C2 | semidirect |
| 7. C2×#121×C173 | C2 | semidirect |
| 35. C2×D692 | D4 | semidirect |
| 46. C2×#13063436 | D4 | semidirect |
| 48. C4⋊Dic173 | D4 | semidirect |
| 60. C2×D4×C173 | D4 | semidirect |
| 71. C4⋊C4×C173 | D4 | semidirect |
| 103. C23×C173 | D8 | semidirect |
| 171. C173 | #1999 | semidirect |
| 175. C2×#121 | D173 | semidirect |
| 221. C2×D4 | C22⋊D173 | semidirect |
| 242. C4⋊C4 | C22⋊D173 | semidirect |
| 265. C23 | #14583811 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149653 | 2 |
| C2×#19149600 | 2 |
| C2×#19149599 | 2 |
| C2×C22⋊#13063436 | 2 |
| #26011253 | 2 |
| C2×#121×C173 | 2 |
| #1999 | 173 |