Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26038456 | C2 | semidirect |
| 3. C2×#19153041 | C2 | semidirect |
| 4. #26038412 | C2 | semidirect |
| 5. #26038209 | C2 | semidirect |
| 6. #26038199 | C2 | semidirect |
| 7. C4×#41×C179 | C2 | semidirect |
| 10. #19153143 | C4 | semidirect |
| 12. #19153138 | C4 | semidirect |
| 33. C2×Dic358 | C2×C4 | semidirect |
| 34. C2×D716 | C2×C4 | semidirect |
| 44. #15668243 | C2×C4 | semidirect |
| 129. C179 | #1906 | semidirect |
| 132. C4×#41 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039237 | 2 |
| #26038456 | 2 |
| C2×#19153041 | 2 |
| #26038412 | 2 |
| #26038209 | 2 |
| #26038199 | 2 |
| C4×#41×C179 | 2 |
| #1906 | 179 |