Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
376 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×M16×D179 | C2 | semidirect |
| 3. C2×#19153040 | C2 | semidirect |
| 4. C4×(C2×D179)⋊C4 | C2 | semidirect |
| 5. #26038200 | C2 | semidirect |
| 6. #26038199 | C2 | semidirect |
| 7. C2×#104×C179 | C2 | semidirect |
| 15. #19153089 | C4 | semidirect |
| 16. #19153089 | C4 | semidirect |
| 17. #19153084 | C4 | semidirect |
| 18. #19153084 | C4 | semidirect |
| 45. #15668243 | D4 | semidirect |
| 73. M16×C179 | D4 | semidirect |
| 139. C2×D179 | #104 | semidirect |
| 159. C179 | #1871 | semidirect |
| 164. C2×#104 | D179 | semidirect |
| 218. M16 | C22⋊D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D179 | 2 |
| #26038946 | 2 |
| C2×#19153040 | 2 |
| C4×(C2×D179)⋊C4 | 2 |
| #26038200 | 2 |
| #26038199 | 2 |
| C2×#104×C179 | 2 |
| #1871 | 179 |