Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
300 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 300 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 |
|---|---|---|
| 1. #24909228 | C2 | semidirect |
| 4. C2×#19127479 | C2 | semidirect |
| 6. #24905548 | C2 | semidirect |
| 7. C83×#1377 | C2 | semidirect |
| 145. #1377 | D83 | semidirect |
| 146. C83 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909228 | 2 |
| #24909090 | 2 |
| #24909083 | 2 |
| C2×#19127479 | 2 |
| #24907307 | 2 |
| #24905548 | 2 |
| C83×#1377 | 2 |
| #13127 | 83 |