Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 133 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. #26041907 | C2 | semidirect |
| 3. #26041585 | C2 | semidirect |
| 4. #26041582 | C2 | semidirect |
| 5. #26041568 | C2 | semidirect |
| 6. #26041563 | C2 | semidirect |
| 7. C2×#19153747 | C2 | semidirect |
| 8. #26041307 | C2 | semidirect |
| 11. #428×C181 | C2 | semidirect |
| 42. #15668449 | Q8 | semidirect |
| 123. C181 | #3084 | semidirect |
| 131. #428 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26041907 | 2 |
| #26041760 | 2 |
| #26041585 | 2 |
| #26041582 | 2 |
| #26041568 | 2 |
| #26041563 | 2 |
| C2×#19153747 | 2 |
| #26041307 | 2 |
| #26041281 | 2 |
| #26041273 | 2 |
| #428×C181 | 2 |
| #3084 | 181 |