Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 171 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. #13125823 | C2 | semidirect |
| 2. #13125300 | C2 | semidirect |
| 3. #13114142 | C2 | semidirect |
| 4. #13114125 | C2 | semidirect |
| 5. #13113460 | C2 | semidirect |
| 6. #13113434 | C2 | semidirect |
| 7. C2×C13×H(3,𝔽4) | C2 | semidirect |
| 19. #11719182 | C22 | semidirect |
| 22. #11718721 | C22 | semidirect |
| 24. #11718719 | C22 | semidirect |
| 25. #11718719 | C22 | semidirect |
| 27. #11718716 | C22 | semidirect |
| 28. #11718587 | C22 | semidirect |
| 29. C4×#6099 | C22 | semidirect |
| 30. #11718132 | C22 | semidirect |
| 31. #11718132 | C22 | semidirect |
| 73. #88128 | C23 | semidirect |
| 75. #88123 | C23 | semidirect |
| 80. #88043 | C23 | semidirect |
| 81. #88043 | C23 | semidirect |
| 139. C2×H(3,𝔽4) | D13 | semidirect |
| 344. C13 | #18992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125823 | 2 |
| #13125300 | 2 |
| #13114142 | 2 |
| #13114125 | 2 |
| #13113460 | 2 |
| #13113434 | 2 |
| C2×C13×H(3,𝔽4) | 2 |
| #18992 | 13 |