Finite Group DatabasebetaFinite Group DatabasebetaOrder 24896.
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×#13095555 | C2 | semidirect |
| 3. #27159452 | C2 | semidirect |
| 4. #27159447 | C2 | semidirect |
| 6. C8×#13095555 | C2 | semidirect |
| 18. #20261955 | C4 | semidirect |
| 19. #20261954 | C4 | semidirect |
| 20. #20261953 | C4 | semidirect |
| 22. SD16×C389 | C4 | semidirect |
| 31. Dic778 | C2×C4 | semidirect |
| 36. #15691005 | C2×C4 | semidirect |
| 37. Q8×C389 | C2×C4 | semidirect |
| 39. C8×C389 | C2×C4 | semidirect |
| 48. #13095555 | SD16 | direct (N × H) |
| 58. C389 | C4×SD16 | semidirect |
| 73. SD16 | #13095555 | direct (N × H) |
| 85. Q8 | C2×#13095555 | semidirect |
| 98. C8 | C2×#13095555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#13095555 | 2 |
| D4×#13095555 | 2 |
| #27159452 | 2 |
| #27159447 | 2 |
| #27159446 | 2 |
| C8×#13095555 | 2 |
| SD16×D389 | 2 |
| C4×SD16 | 389 |