Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 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. #24905664 | C2 | semidirect |
| 3. #24905640 | C2 | semidirect |
| 4. C22⋊(C83⋊C32) | C2 | semidirect |
| 5. C2×#366×C83 | C2 | semidirect |
| 78. C2×#366 | D83 | semidirect |
| 82. C83 | #13712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909549 | 2 |
| #24905664 | 2 |
| #24905640 | 2 |
| C22⋊(C83⋊C32) | 2 |
| C2×#366×C83 | 2 |
| #13712 | 83 |