Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1066 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1066 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. #13125839 | C2 | semidirect |
| 2. #13125222 | C2 | semidirect |
| 3. #13114142 | C2 | semidirect |
| 4. #13113460 | C2 | semidirect |
| 5. #13113434 | C2 | semidirect |
| 16. #11719175 | C22 | semidirect |
| 21. #11718721 | C22 | semidirect |
| 23. #11718716 | C22 | semidirect |
| 24. #11718716 | C22 | semidirect |
| 26. #11718587 | C22 | semidirect |
| 27. C4×#6099 | C22 | semidirect |
| 28. #11718132 | C22 | semidirect |
| 29. #11718132 | C22 | semidirect |
| 65. #88123 | C23 | semidirect |
| 73. #88043 | C23 | semidirect |
| 74. #88043 | C23 | semidirect |
| 306. C13 | #18997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125839 | 2 |
| #13125222 | 2 |
| #13114142 | 2 |
| #13113460 | 2 |
| #13113434 | 2 |
| C2×C13×H(3,𝔽4) | 2 |
| #18997 | 13 |