Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
216 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 216 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 |
|---|---|---|
| 1. C2×#19127539 | C2 | semidirect |
| 3. #24909724 | C2 | semidirect |
| 4. C4⋊(C83⋊C32) | C2 | semidirect |
| 5. #24905643 | C2 | semidirect |
| 6. #24905640 | C2 | semidirect |
| 7. C4×D16×C83 | C2 | semidirect |
| 101. C4×D16 | D83 | semidirect |
| 105. C83 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127539 | 2 |
| C2×#19127536 | 2 |
| #24909724 | 2 |
| C4⋊(C83⋊C32) | 2 |
| #24905643 | 2 |
| #24905640 | 2 |
| C4×D16×C83 | 2 |
| #13689 | 83 |