Finite Group DatabasebetaFinite Group DatabasebetaOrder 33472.
270 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. C2×Q8×D523 | C2 | semidirect |
| 3. #30660372 | C2 | semidirect |
| 4. #30660359 | C2 | semidirect |
| 5. #30660358 | C2 | semidirect |
| 6. #30660355 | C2 | semidirect |
| 7. #30660353 | C2 | semidirect |
| 8. #30660352 | C2 | semidirect |
| 9. #30660349 | C2 | semidirect |
| 10. #30660331 | C2 | semidirect |
| 11. C22⋊Q8×C523 | C2 | semidirect |
| 83. C523 | #536 | semidirect |
| 94. C22⋊Q8 | D523 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552641 | 2 |
| C2×Q8×D523 | 2 |
| #30660372 | 2 |
| #30660359 | 2 |
| #30660358 | 2 |
| #30660355 | 2 |
| #30660353 | 2 |
| #30660352 | 2 |
| #30660349 | 2 |
| #30660331 | 2 |
| C22⋊Q8×C523 | 2 |
| #536 | 523 |