Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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. #26038879 | C2 | semidirect |
| 3. C2×#19153058 | C2 | semidirect |
| 4. #26038715 | C2 | semidirect |
| 5. #26038251 | C2 | semidirect |
| 6. #26038222 | C2 | semidirect |
| 7. #359×C179 | C2 | semidirect |
| 13. C2×Dic716 | C22 | semidirect |
| 20. #19153053 | C22 | semidirect |
| 23. C2×C16×C179 | C22 | semidirect |
| 24. #108×C179 | C22 | semidirect |
| 91. C179 | #2194 | semidirect |
| 98. #359 | D179 | semidirect |
| 114. C2×C16 | 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 |
|---|---|
| #26039241 | 2 |
| #26038879 | 2 |
| C2×#19153058 | 2 |
| #26038715 | 2 |
| #26038251 | 2 |
| #26038222 | 2 |
| #359×C179 | 2 |
| #2194 | 179 |