Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1568 conjugacy classes of subgroups; only the 621 normal subgroups are shown.
This group has 1568 conjugacy classes of subgroups — too many to draw. Only its 621 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. C22×Q8×D31 | C2 | semidirect |
| 2. Q8×D124 | C2 | direct (N × H) |
| 3. C2×#11758446 | C2 | semidirect |
| 4. C2×#11758474 | C2 | semidirect |
| 6. C2×C4×Q8×C31 | C2 | semidirect |
| 9. C2×Q8×D31 | C22 | semidirect |
| 13. C4×Q8×C31 | C22 | semidirect |
| 19. #11758474 | C22 | semidirect |
| 21. #11758446 | C22 | semidirect |
| 23. C2×Q8×C31 | D4 | semidirect |
| 30. C2×D124 | Q8 | direct (N × H) |
| 44. C22×D31 | C2×Q8 | semidirect |
| 46. Q8×C31 | C2×D4 | semidirect |
| 49. C2×C4×C31 | C2×Q8 | semidirect |
| 55. D124 | C2×Q8 | direct (N × H) |
| 66. C2×D31 | C22×Q8 | semidirect |
| 69. C4×C31 | C22×Q8 | semidirect |
| 75. C2×C4×Q8 | D31 | semidirect |
| 77. C2×C31 | D4×Q8 | semidirect |
| 90. C4×Q8 | C2×D31 | semidirect |
| 97. C31 | C2×D4×Q8 | semidirect |
| 102. C2×Q8 | D124 | direct (N × H) |
| 123. Q8 | C2×D124 | direct (N × H) |
| 130. C2×C4 | Q8×D31 | semidirect |
| 145. C4 | C2×Q8×D31 | semidirect |
| 147. C2 | Q8×D124 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D31 | 2 |
| Q8×D124 | 2 |
| C2×#11758446 | 2 |
| C2×#11758474 | 2 |
| C2×C4×D124 | 2 |
| C2×C4×Q8×C31 | 2 |
| C2×D4×Q8 | 31 |