Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
366 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19127531 | C2 | semidirect |
| 4. #24905571 | C2 | semidirect |
| 5. C2×#367×C83 | C2 | semidirect |
| 8. #19128117 | C4 | semidirect |
| 122. C2×#367 | D83 | semidirect |
| 125. C83 | #12843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128117 | 2 |
| C2×#19127531 | 2 |
| #24907528 | 2 |
| #24905571 | 2 |
| C2×#367×C83 | 2 |
| #12843 | 83 |