Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
348 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 3. C2×#19153871 | C2 | semidirect |
| 4. C2×C4×#13089685 | C2 | semidirect |
| 5. #26042145 | C2 | semidirect |
| 6. #26042145 | C2 | semidirect |
| 10. C2×#15668459 | C4 | semidirect |
| 15. #19153873 | C4 | semidirect |
| 60. #13089685 | C22⋊C4 | semidirect |
| 73. C2×Dic181 | M16 | semidirect |
| 93. C2×C4×C181 | M16 | semidirect |
| 125. C181 | #1753 | semidirect |
| 215. C2×C4 | #15668459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668459 | 2 |
| C2×#19153873 | 2 |
| C2×#19153871 | 2 |
| C2×C4×#13089685 | 2 |
| #26042145 | 2 |
| #26041126 | 2 |
| #1753 | 181 |