Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
280 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 91 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. #24909738 | C2 | semidirect |
| 3. #24909691 | C2 | semidirect |
| 5. #24907060 | C2 | semidirect |
| 7. C83×#1311 | C2 | semidirect |
| 68. C16×C83 | SD16 | semidirect |
| 110. #1311 | D83 | semidirect |
| 111. C83 | #12508 | semidirect |
| 172. C16 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24909738 | 2 |
| #24909719 | 2 |
| #24909691 | 2 |
| #24909687 | 2 |
| #24907060 | 2 |
| #24907055 | 2 |
| C83×#1311 | 2 |
| #12508 | 83 |