Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 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×#13093637 | C2 | semidirect |
| 3. #26045860 | C2 | semidirect |
| 4. #26045855 | C2 | semidirect |
| 6. C8×#13093637 | C2 | semidirect |
| 18. #20238599 | C4 | semidirect |
| 19. #20238598 | C4 | semidirect |
| 20. #20238597 | C4 | semidirect |
| 22. SD16×C373 | C4 | semidirect |
| 31. Dic746 | C2×C4 | semidirect |
| 36. #15688412 | C2×C4 | semidirect |
| 37. Q8×C373 | C2×C4 | semidirect |
| 39. C8×C373 | C2×C4 | semidirect |
| 48. #13093637 | SD16 | direct (N × H) |
| 58. C373 | C4×SD16 | semidirect |
| 73. SD16 | #13093637 | direct (N × H) |
| 85. Q8 | C2×#13093637 | semidirect |
| 98. C8 | C2×#13093637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13093637 | 2 |
| D4×#13093637 | 2 |
| #26045860 | 2 |
| #26045855 | 2 |
| #26045854 | 2 |
| C8×#13093637 | 2 |
| SD16×D373 | 2 |
| C4×SD16 | 373 |