Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 370 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. #26042009 | C2 | semidirect |
| 3. #26041676 | C2 | semidirect |
| 4. #26041675 | C2 | semidirect |
| 6. #26041565 | C2 | semidirect |
| 7. #26041563 | C2 | semidirect |
| 8. #26041403 | C2 | semidirect |
| 48. #15668437 | Q8 | semidirect |
| 77. Dic362 | SD16 | semidirect |
| 78. Dic362 | C2×Q8 | semidirect |
| 86. #13089678 | C2×Q8 | semidirect |
| 117. C181 | Q8×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042009 | 2 |
| D4×Dic362 | 2 |
| #26041676 | 2 |
| #26041675 | 2 |
| #26041567 | 2 |
| #26041565 | 2 |
| #26041563 | 2 |
| #26041403 | 2 |
| #26041370 | 2 |
| C4×#15668437 | 2 |
| #476×C181 | 2 |
| Q8×SD16 | 181 |