Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 4. M16×Dic179 | C2 | semidirect |
| 5. C42×Dic179 | C2 | semidirect |
| 6. #26038198 | C2 | semidirect |
| 7. #339×C179 | C2 | semidirect |
| 10. #19153078 | C4 | semidirect |
| 11. #19153075 | C4 | semidirect |
| 18. #19153041 | C4 | semidirect |
| 19. #19153039 | C4 | semidirect |
| 37. #15668243 | C2×C4 | semidirect |
| 45. C4×Dic179 | C2×C4 | semidirect |
| 51. M16×C179 | C2×C4 | semidirect |
| 57. C42×C179 | C2×C4 | semidirect |
| 60. Dic358 | C42 | semidirect |
| 62. D716 | C42 | semidirect |
| 101. Dic179 | #104 | semidirect |
| 107. C179 | C4×#104 | semidirect |
| 115. #339 | D179 | semidirect |
| 149. M16 | C4×D179 | semidirect |
| 165. C42 | C4×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26038907 | 2 |
| C2×#19153041 | 2 |
| C2×#19153039 | 2 |
| M16×Dic179 | 2 |
| C42×Dic179 | 2 |
| #26038198 | 2 |
| #339×C179 | 2 |
| C4×#104 | 179 |