Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #30659756 | C2 | semidirect |
| 2. #30659755 | C2 | semidirect |
| 3. #30659741 | C2 | semidirect |
| 4. #30659740 | C2 | semidirect |
| 5. #30659737 | C2 | semidirect |
| 6. #30659729 | C2 | semidirect |
| 7. #30659728 | C2 | semidirect |
| 8. C2×#22552354 | C2 | semidirect |
| 9. Q16×D521 | C2 | semidirect |
| 10. #30659716 | C2 | semidirect |
| 11. #137×C521 | C2 | semidirect |
| 87. C521 | #578 | semidirect |
| 94. #137 | D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30659756 | 2 |
| #30659755 | 2 |
| #30659741 | 2 |
| #30659740 | 2 |
| #30659737 | 2 |
| #30659729 | 2 |
| #30659728 | 2 |
| C2×#22552354 | 2 |
| Q16×D521 | 2 |
| #30659716 | 2 |
| #137×C521 | 2 |
| #578 | 521 |