Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
234 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 71 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. #24907081 | C2 | semidirect |
| 4. #24905520 | C2 | semidirect |
| 5. C83×#1370 | C2 | semidirect |
| 39. D664 | Q16 | semidirect |
| 90. #1370 | D83 | semidirect |
| 92. C83 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909611 | 2 |
| #24907081 | 2 |
| C8×D664 | 2 |
| #24905520 | 2 |
| C83×#1370 | 2 |
| #12447 | 83 |