Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1022 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 199 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×D13×D16 | C2 | semidirect |
| 2. D13×#493 | C2 | semidirect |
| 3. #13117086 | C2 | semidirect |
| 4. #13117085 | C2 | semidirect |
| 5. #13117084 | C2 | semidirect |
| 6. C4×C16×D13 | C2 | semidirect |
| 7. C13×#2246 | C2 | semidirect |
| 11. C2×C13×D16 | C22 | semidirect |
| 12. C13×#493 | C22 | semidirect |
| 14. #11718812 | C22 | semidirect |
| 15. C2×#88066 | C22 | semidirect |
| 18. C2×D208 | C22 | semidirect |
| 20. #11718356 | C22 | semidirect |
| 22. C4×C13×C16 | C22 | semidirect |
| 23. C16×Dic13 | C22 | semidirect |
| 24. C4×#6090 | C22 | semidirect |
| 51. C16×D13 | D4 | semidirect |
| 80. C13×C16 | C2×D4 | semidirect |
| 81. #6090 | C2×D4 | semidirect |
| 87. #2246 | D13 | direct (N × H) |
| 106. C4×D13 | D16 | semidirect |
| 119. C2×D16 | C2×D13 | semidirect |
| 125. #493 | C2×D13 | semidirect |
| 129. C4×C16 | C2×D13 | semidirect |
| 138. C4×C13 | C2×D16 | semidirect |
| 142. Dic13 | C2×D16 | semidirect |
| 174. D13 | #2246 | direct (N × H) |
| 203. C16 | D4×D13 | semidirect |
| 204. C13 | C2×#2246 | semidirect |
| 239. C4 | D13×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D13×D16 | 2 |
| D13×#493 | 2 |
| #13117086 | 2 |
| #13117085 | 2 |
| #13117084 | 2 |
| C4×C16×D13 | 2 |
| C13×#2246 | 2 |
| C2×#2246 | 13 |