Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#19153881 | C2 | semidirect |
| 2. C2×#19153880 | C2 | semidirect |
| 3. C4×#15668459 | C2 | semidirect |
| 4. C4×C4⋊#10624382 | C2 | semidirect |
| 16. #19153814 | C4 | semidirect |
| 17. #19153812 | C4 | semidirect |
| 18. #19153804 | C4 | semidirect |
| 24. #124×C181 | C4 | semidirect |
| 27. #15668459 | D4 | semidirect |
| 108. Dic181 | #104 | semidirect |
| 117. C181 | #1980 | semidirect |
| 130. #124 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19153881 | 2 |
| C2×#19153880 | 2 |
| C4×#15668459 | 2 |
| C4×C4⋊#10624382 | 2 |
| #26041828 | 2 |
| #1980 | 181 |