Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
572 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 97 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. C22×#14581733 | C2 | semidirect |
| 2. C2×#19127968 | C2 | semidirect |
| 3. #24917112 | C2 | semidirect |
| 4. C2×#19127515 | C2 | semidirect |
| 5. C2×#19127486 | C2 | semidirect |
| 6. #24905558 | C2 | semidirect |
| 7. C83×#2140 | C2 | semidirect |
| 56. C2×C83⋊C16 | D4 | semidirect |
| 58. #14581728 | D4 | semidirect |
| 67. C2×D8×C83 | D4 | semidirect |
| 204. #2140 | D83 | semidirect |
| 207. C83 | #13319 | semidirect |
| 247. C2×D8 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14581733 | 2 |
| C2×#19127968 | 2 |
| #24917112 | 2 |
| C2×#19127515 | 2 |
| C2×#19127486 | 2 |
| #24905558 | 2 |
| C83×#2140 | 2 |
| #13319 | 83 |