Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
578 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 163 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. #24918042 | C2 | semidirect |
| 2. #24909601 | C2 | semidirect |
| 3. #24909549 | C2 | semidirect |
| 4. #24909499 | C2 | semidirect |
| 5. C2×C4⋊C16×C83 | C2 | semidirect |
| 73. C2×C4×C83 | D16 | semidirect |
| 113. C2×C4⋊C16 | D83 | semidirect |
| 114. C83 | #33811 | semidirect |
| 190. C2×C4 | D1328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918042 | 2 |
| #24909601 | 2 |
| #24909549 | 2 |
| #24909499 | 2 |
| C2×C4⋊C16×C83 | 2 |
| #33811 | 83 |