Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
384 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 2. C2×#19149612 | C2 | semidirect |
| 3. C2×#19149601 | C2 | semidirect |
| 4. C2×C8×Dic173 | C2 | semidirect |
| 5. #26011394 | C2 | semidirect |
| 6. #26011392 | C2 | semidirect |
| 7. C2×#102×C173 | C2 | semidirect |
| 11. C2×#14583811 | C4 | semidirect |
| 70. C2×Dic173 | D8 | semidirect |
| 71. #13063436 | C22⋊C4 | semidirect |
| 120. C173 | #1970 | semidirect |
| 125. C2×#102 | D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14583811 | 2 |
| C2×#19149612 | 2 |
| C2×#19149601 | 2 |
| C2×C8×Dic173 | 2 |
| #26011394 | 2 |
| #26011392 | 2 |
| C2×#102×C173 | 2 |
| #1970 | 173 |