Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #24909272 | C2 | semidirect |
| 3. #24907610 | C2 | semidirect |
| 4. #24905455 | C2 | semidirect |
| 5. #24905454 | C2 | semidirect |
| 6. #24905447 | C2 | semidirect |
| 7. C83×#1339 | C2 | semidirect |
| 9. #19128098 | C4 | semidirect |
| 10. #19128076 | C4 | semidirect |
| 14. #19127813 | C4 | semidirect |
| 15. #19127812 | C4 | semidirect |
| 155. #1339 | D83 | semidirect |
| 156. C83 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918196 | 2 |
| #24909272 | 2 |
| #24907610 | 2 |
| #24905455 | 2 |
| #24905454 | 2 |
| #24905447 | 2 |
| C83×#1339 | 2 |
| #11837 | 83 |