Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #26038907 | C2 | semidirect |
| 3. #26038455 | C2 | semidirect |
| 4. C2×#19153039 | C2 | semidirect |
| 5. #26038412 | C2 | semidirect |
| 6. #26038200 | C2 | semidirect |
| 7. #344×C179 | C2 | semidirect |
| 11. #19153146 | C4 | semidirect |
| 13. #19153141 | C4 | semidirect |
| 37. C2×Dic358 | C2×C4 | semidirect |
| 39. C2×D716 | C2×C4 | semidirect |
| 64. M16×C179 | C2×C4 | semidirect |
| 129. C179 | #1906 | semidirect |
| 136. #344 | D179 | semidirect |
| 185. M16 | C4×D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039239 | 2 |
| #26038907 | 2 |
| #26038455 | 2 |
| C2×#19153039 | 2 |
| #26038412 | 2 |
| #26038200 | 2 |
| #344×C179 | 2 |
| #1906 | 179 |