Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
370 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 141 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. Q8×Dic362 | C2 | semidirect |
| 3. #26041677 | C2 | semidirect |
| 4. #26041676 | C2 | semidirect |
| 7. #26041564 | C2 | semidirect |
| 8. #26041562 | C2 | semidirect |
| 9. C8×Dic362 | C2 | semidirect |
| 64. SD16×C181 | Q8 | semidirect |
| 77. Dic362 | SD16 | direct (N × H) |
| 86. Q8×C181 | C2×Q8 | semidirect |
| 97. C8×C181 | C2×Q8 | semidirect |
| 117. C181 | Q8×SD16 | semidirect |
| 169. SD16 | Dic362 | direct (N × H) |
| 198. Q8 | C2×Dic362 | semidirect |
| 215. C8 | C2×Dic362 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic362 | 2 |
| D4×Dic362 | 2 |
| #26041677 | 2 |
| #26041676 | 2 |
| #26041569 | 2 |
| #26041567 | 2 |
| #26041564 | 2 |
| #26041562 | 2 |
| C8×Dic362 | 2 |
| SD16×Dic181 | 2 |
| C4×SD16×C181 | 2 |
| Q8×SD16 | 181 |