Finite Group DatabasebetaFinite Group DatabasebetaOrder 3968.
1504 conjugacy classes of subgroups; only the 525 normal subgroups are shown.
This group has 1504 conjugacy classes of subgroups — too many to draw. Only its 525 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×#92499 | C2 | semidirect |
| 2. C2×#11758496 | C2 | direct (N × H) |
| 3. C22×#92481 | C2 | semidirect |
| 4. C22×D248 | C2 | semidirect |
| 5. C22×C8×D31 | C2 | semidirect |
| 6. C22×Q16×C31 | C2 | semidirect |
| 9. C2×#92499 | C22 | semidirect |
| 14. C2×Q16×C31 | C22 | semidirect |
| 16. C2×#92481 | C22 | semidirect |
| 18. #11758496 | C22 | direct (N × H) |
| 19. C2×D248 | C22 | semidirect |
| 20. C2×C8×D31 | C22 | semidirect |
| 29. #92499 | C23 | semidirect |
| 36. Q16×C31 | C23 | semidirect |
| 38. #92481 | C23 | semidirect |
| 40. D248 | C23 | semidirect |
| 41. C8×D31 | C23 | semidirect |
| 62. C22×C31 | #135 | semidirect |
| 74. C22×Q16 | D31 | semidirect |
| 78. C2×C31 | C2×#135 | semidirect |
| 90. C2×Q16 | C2×D31 | semidirect |
| 96. C31 | C22×#135 | semidirect |
| 112. Q16 | C22×D31 | semidirect |
| 141. C22 | #11758496 | direct (N × H) |
| 149. C2 | C2×#11758496 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#92499 | 2 |
| C2×#11758496 | 2 |
| C22×#92481 | 2 |
| C22×D248 | 2 |
| C22×C8×D31 | 2 |
| C22×Q16×C31 | 2 |
| C22×#135 | 31 |