Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
320 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 95 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. #24909260 | C2 | semidirect |
| 3. C4⋊C16×D83 | C2 | semidirect |
| 4. Q8⋊(C83⋊C16) | C2 | semidirect |
| 5. #24905419 | C2 | semidirect |
| 6. #24905417 | C2 | semidirect |
| 7. C83×Q8⋊C16 | C2 | semidirect |
| 158. Q8⋊C16 | D83 | semidirect |
| 161. C83 | #11622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24916440 | 2 |
| #24909260 | 2 |
| C4⋊C16×D83 | 2 |
| Q8⋊(C83⋊C16) | 2 |
| #24905419 | 2 |
| #24905417 | 2 |
| C83×Q8⋊C16 | 2 |
| #11622 | 83 |