Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #30659703 | C2 | semidirect |
| 2. #30659699 | C2 | semidirect |
| 3. #30659698 | C2 | semidirect |
| 5. #30659688 | C2 | semidirect |
| 6. #30659687 | C2 | semidirect |
| 7. #30659673 | C2 | semidirect |
| 9. #30659667 | C2 | semidirect |
| 10. #30659666 | C2 | semidirect |
| 11. C2×C4⋊C4×C521 | C2 | semidirect |
| 72. C521 | #552 | semidirect |
| 84. C2×C4⋊C4 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659703 | 2 |
| #30659699 | 2 |
| #30659698 | 2 |
| #30659691 | 2 |
| #30659688 | 2 |
| #30659687 | 2 |
| #30659673 | 2 |
| C4×C22⋊D521 | 2 |
| #30659667 | 2 |
| #30659666 | 2 |
| C2×C4⋊C4×C521 | 2 |
| #552 | 521 |