Finite Group DatabasebetaFinite Group DatabasebetaOrder 22912.
344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. #26039205 | C2 | semidirect |
| 3. #26038445 | C2 | semidirect |
| 4. #26038443 | C2 | semidirect |
| 5. #26038412 | C2 | semidirect |
| 6. #26038195 | C2 | semidirect |
| 7. H(3,ℤ/4)×C179 | C2 | semidirect |
| 14. #19153110 | C4 | semidirect |
| 15. #19153101 | C4 | semidirect |
| 44. C2×C179⋊C8 | D4 | semidirect |
| 53. C2×C8×C179 | D4 | semidirect |
| 115. C179 | #1910 | semidirect |
| 123. H(3,ℤ/4) | D179 | semidirect |
| 165. C2×C8 | D716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26039205 | 2 |
| #26039008 | 2 |
| #26038445 | 2 |
| #26038443 | 2 |
| #26038412 | 2 |
| #26038195 | 2 |
| H(3,ℤ/4)×C179 | 2 |
| #1910 | 179 |