Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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. #24909365 | C2 | semidirect |
| 4. #24905441 | C2 | semidirect |
| 6. #24905380 | C2 | semidirect |
| 7. C83×#1367 | C2 | semidirect |
| 59. C83⋊C16 | SD16 | semidirect |
| 80. Dic166 | M32 | semidirect |
| 109. #1367 | D83 | semidirect |
| 113. C83 | #12050 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909365 | 2 |
| #24909294 | 2 |
| C8×#13050579 | 2 |
| #24905441 | 2 |
| #24905417 | 2 |
| #24905380 | 2 |
| C83×#1367 | 2 |
| #12050 | 83 |