Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 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. #26012542 | C2 | semidirect |
| 2. #26012522 | C2 | semidirect |
| 3. D4×#13063443 | C2 | semidirect |
| 4. #26012511 | C2 | semidirect |
| 5. #26012508 | C2 | semidirect |
| 6. #26012494 | C2 | semidirect |
| 7. C2×#19149746 | C2 | semidirect |
| 79. D4×C173 | M16 | semidirect |
| 107. C173 | #2990 | semidirect |
| 172. D4 | #14583835 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26012542 | 2 |
| #26012522 | 2 |
| D4×#13063443 | 2 |
| #26012511 | 2 |
| #26012508 | 2 |
| #26012494 | 2 |
| C2×#19149746 | 2 |
| #41×Dic173 | 2 |
| #2990 | 173 |