Finite Group DatabasebetaFinite Group DatabasebetaOrder 3392.
198 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 45 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. C2×D4×D53 | C2 | semidirect |
| 2. C2×D424 | C2 | semidirect |
| 3. C2×#11719922 | C2 | semidirect |
| 4. #13133192 | C2 | semidirect |
| 5. #13133137 | C2 | semidirect |
| 6. #13133129 | C2 | semidirect |
| 7. #102×C53 | C2 | semidirect |
| 15. C2×D212 | C22 | semidirect |
| 17. C2×C8×C53 | C22 | semidirect |
| 18. C4⋊C4×C53 | C22 | semidirect |
| 21. C2×#88322 | C22 | semidirect |
| 31. D4×C53 | D4 | semidirect |
| 40. D212 | D4 | semidirect |
| 58. C2×D53 | D8 | semidirect |
| 71. C53 | #447 | semidirect |
| 77. #102 | D53 | semidirect |
| 91. C2×C8 | C2×D53 | semidirect |
| 92. C4⋊C4 | C2×D53 | semidirect |
| 108. D4 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D53 | 2 |
| C2×D424 | 2 |
| C2×#11719922 | 2 |
| #13133192 | 2 |
| #13133137 | 2 |
| #13133129 | 2 |
| #102×C53 | 2 |
| #447 | 53 |