Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
234 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 103 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. #30659702 | C2 | semidirect |
| 2. #30659700 | C2 | semidirect |
| 3. #30659696 | C2 | semidirect |
| 4. #30659691 | C2 | semidirect |
| 5. #30659687 | C2 | semidirect |
| 7. C4×Dic1042 | C2 | semidirect |
| 8. C4×D2084 | C2 | semidirect |
| 9. C4×C22⋊D521 | C2 | semidirect |
| 10. #30659665 | C2 | semidirect |
| 11. C2×C42×C521 | C2 | semidirect |
| 74. C521 | #529 | semidirect |
| 86. C2×C42 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659702 | 2 |
| #30659700 | 2 |
| #30659696 | 2 |
| #30659691 | 2 |
| #30659687 | 2 |
| #30659682 | 2 |
| C4×Dic1042 | 2 |
| C4×D2084 | 2 |
| C4×C22⋊D521 | 2 |
| #30659665 | 2 |
| C2×C42×C521 | 2 |
| #529 | 521 |