Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
270 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 79 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. C2×#19127536 | C2 | semidirect |
| 2. #24909713 | C2 | semidirect |
| 3. C4×C83⋊C32 | C2 | semidirect |
| 4. C83×#2246 | C2 | semidirect |
| 19. C83⋊C32 | D4 | semidirect |
| 61. C4×C83 | D32 | semidirect |
| 71. #2246 | D83 | semidirect |
| 73. C83 | #13725 | semidirect |
| 130. C4 | #19127536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19127536 | 2 |
| #24909713 | 2 |
| C4×C83⋊C32 | 2 |
| C83×#2246 | 2 |
| #13725 | 83 |