Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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. #26042283 | C2 | semidirect |
| 2. C2×#19153881 | C2 | semidirect |
| 3. C2×#19153880 | C2 | semidirect |
| 4. #26042215 | C2 | semidirect |
| 14. #19153814 | C4 | semidirect |
| 15. #19153812 | C4 | semidirect |
| 16. #19153804 | C4 | semidirect |
| 20. #124×C181 | C4 | semidirect |
| 26. C4×#10624382 | D4 | semidirect |
| 94. C181 | #1963 | semidirect |
| 107. #124 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042283 | 2 |
| C2×#19153881 | 2 |
| C2×#19153880 | 2 |
| #26042215 | 2 |
| #26041828 | 2 |
| #1963 | 181 |