Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
512 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×C4⋊Dic23 | C2 | semidirect |
| 2. #13092728 | C2 | direct (N × H) |
| 3. C2×#10624989 | C2 | semidirect |
| 4. C2×#10625014 | C2 | semidirect |
| 5. C2×C22⋊(C23⋊C8) | C2 | semidirect |
| 18. C2×C4⋊Dic23 | C22 | semidirect |
| 20. #10625014 | C22 | semidirect |
| 21. C22⋊(C23⋊C8) | C22 | semidirect |
| 22. #10624989 | C22 | semidirect |
| 98. C2×C23 | #480 | semidirect |
| 118. C23 | C2×#480 | semidirect |
| 187. C2 | #13092728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic23 | 2 |
| #13092728 | 2 |
| C2×#10624989 | 2 |
| C2×#10625014 | 2 |
| C2×C22⋊(C23⋊C8) | 2 |
| C2×C23×#121 | 2 |
| C2×#480 | 23 |