Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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×#22552363 | C2 | semidirect |
| 2. C2×#22552352 | C2 | semidirect |
| 3. #30659679 | C2 | semidirect |
| 4. #30659633 | C2 | semidirect |
| 5. #30659629 | C2 | semidirect |
| 6. #30659620 | C2 | semidirect |
| 7. C2×D8×C521 | C2 | semidirect |
| 25. Dic1042 | D4 | semidirect |
| 40. D4×C521 | D4 | semidirect |
| 64. C521 | #449 | semidirect |
| 68. C2×D8 | D521 | semidirect |
| 98. D4 | C22⋊D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552363 | 2 |
| C2×#22552352 | 2 |
| #30659679 | 2 |
| #30659633 | 2 |
| #30659629 | 2 |
| #30659620 | 2 |
| C2×D8×C521 | 2 |
| #449 | 521 |