Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #26038880 | C2 | semidirect |
| 3. C2×#19153056 | C2 | semidirect |
| 4. #26038251 | C2 | semidirect |
| 5. #26038245 | C2 | semidirect |
| 6. #26038223 | C2 | semidirect |
| 7. #473×C179 | C2 | semidirect |
| 18. #19153053 | C22 | semidirect |
| 19. C2×C179⋊C16 | C22 | semidirect |
| 21. C2×Q16×C179 | C22 | semidirect |
| 23. #108×C179 | C22 | semidirect |
| 91. C179 | #2194 | semidirect |
| 96. #473 | D179 | semidirect |
| 106. C2×Q16 | C2×D179 | semidirect |
| 115. #108 | C2×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039244 | 2 |
| #26038880 | 2 |
| C2×#19153056 | 2 |
| #26038251 | 2 |
| #26038245 | 2 |
| #26038223 | 2 |
| #473×C179 | 2 |
| #2194 | 179 |