Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
120 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 42 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. #26045861 | C2 | semidirect |
| 4. #26045855 | C2 | semidirect |
| 6. #26045846 | 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 |
| 58. C373 | #440 | semidirect |
| 73. SD16 | #13093637 | semidirect |
| 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 |
| #26045861 | 2 |
| #26045855 | 2 |
| #26045854 | 2 |
| #26045846 | 2 |
| SD16×D373 | 2 |
| #440 | 373 |