Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
480 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 2. #26042319 | C2 | direct (N × H) |
| 18. C2×Dic724 | C4 | semidirect |
| 19. C2×#15668439 | C4 | semidirect |
| 20. Q16×D181 | C4 | semidirect |
| 23. C2×Q16×C181 | C4 | semidirect |
| 43. Dic724 | C2×C4 | semidirect |
| 44. #15668439 | C2×C4 | semidirect |
| 49. Q16×C181 | C2×C4 | semidirect |
| 87. C2×C181 | #441 | semidirect |
| 89. D181 | #441 | semidirect |
| 91. C181 | C2×#441 | semidirect |
| 104. C2×Q16 | #10624382 | semidirect |
| 129. Q16 | C2×#10624382 | semidirect |
| 181. C2 | #26042319 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| #26042319 | 2 |
| C2×#19153884 | 2 |
| C2×#19153879 | 2 |
| C2×#19153870 | 2 |
| C2×Q16×D181 | 2 |
| C2×#441 | 181 |