Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 158 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. #26012541 | C2 | semidirect |
| 2. #26012523 | C2 | semidirect |
| 3. #26012519 | C2 | semidirect |
| 4. #26012514 | C2 | semidirect |
| 5. #26012508 | C2 | semidirect |
| 6. #26012494 | C2 | semidirect |
| 7. D173⋊(C4⋊C8) | C2 | semidirect |
| 65. D692 | M16 | semidirect |
| 107. C173 | #2990 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012541 | 2 |
| #26012523 | 2 |
| #26012519 | 2 |
| #26012514 | 2 |
| #26012508 | 2 |
| #26012494 | 2 |
| D173⋊(C4⋊C8) | 2 |
| #26011959 | 2 |
| #2990 | 173 |