Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×D212 | C2 | semidirect |
| 2. #13133242 | C2 | direct (N × H) |
| 3. C2×#11719924 | C2 | semidirect |
| 4. C2×#11719922 | C2 | semidirect |
| 5. C2×#11719917 | C2 | semidirect |
| 6. C2×#41×C53 | C2 | semidirect |
| 9. #41×C53 | C22 | semidirect |
| 10. C2×Q8×C53 | C22 | semidirect |
| 12. C2×D4×C53 | C22 | semidirect |
| 18. C2×D212 | C22 | semidirect |
| 19. #11719924 | C22 | semidirect |
| 20. #11719922 | C22 | semidirect |
| 21. #11719917 | C22 | semidirect |
| 22. C2×#88322 | C22 | semidirect |
| 29. Q8×C53 | C23 | semidirect |
| 32. D4×C53 | C23 | semidirect |
| 42. #88322 | C23 | semidirect |
| 57. C2×C53 | AGL(1,ℤ/8) | semidirect |
| 61. C53 | C2×AGL(1,ℤ/8) | semidirect |
| 62. C2×#41 | D53 | semidirect |
| 70. #41 | C2×D53 | semidirect |
| 71. C2×Q8 | C2×D53 | semidirect |
| 77. C2×D4 | C2×D53 | semidirect |
| 90. Q8 | C22×D53 | semidirect |
| 96. D4 | C22×D53 | semidirect |
| 119. C2 | #13133242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D212 | 2 |
| #13133242 | 2 |
| C2×#11719924 | 2 |
| C2×#11719922 | 2 |
| C2×#11719917 | 2 |
| C2×#41×C53 | 2 |
| C2×AGL(1,ℤ/8) | 53 |