Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
548 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 121 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. #13092434 | C2 | semidirect |
| 2. #13092413 | C2 | semidirect |
| 3. #13092391 | C2 | semidirect |
| 4. #13092384 | C2 | semidirect |
| 7. C23×2−1+4 | C4 | semidirect |
| 10. C23×H(5,𝔽2) | C4 | semidirect |
| 15. #10625097 | C22 | semidirect |
| 16. C2×#67267 | C22 | semidirect |
| 17. C22×C23⋊C8 | C22 | semidirect |
| 115. 2−1+4 | Dic23 | semidirect |
| 118. H(5,𝔽2) | Dic23 | semidirect |
| 131. C23 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13092434 | 2 |
| #13092413 | 2 |
| #13092391 | 2 |
| #13092384 | 2 |
| C23×#585 | 2 |
| #1794 | 23 |