Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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. #26011548 | C2 | semidirect |
| 2. C4×#14583810 | C2 | semidirect |
| 3. D4⋊#13063436 | C2 | semidirect |
| 6. C4⋊#13063436 | C22 | semidirect |
| 10. C4×#13063436 | C22 | semidirect |
| 51. D4×C173 | M16 | semidirect |
| 85. C173 | #1490 | semidirect |
| 135. D4 | #14583810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26011548 | 2 |
| C4×#14583810 | 2 |
| D4⋊#13063436 | 2 |
| C2×C4×D4×C173 | 2 |
| #1490 | 173 |