Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
794 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 139 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×#19128078 | C2 | semidirect |
| 2. C2×#19127896 | C2 | semidirect |
| 3. C2×#19127444 | C2 | semidirect |
| 4. #24905298 | C2 | semidirect |
| 5. C83×#1954 | C2 | semidirect |
| 71. C2×D4×C83 | D8 | semidirect |
| 84. C2×C8×C83 | D8 | semidirect |
| 161. #1954 | D83 | semidirect |
| 164. C83 | #10260 | semidirect |
| 225. C2×D4 | D664 | semidirect |
| 243. C2×C8 | #13050575 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128078 | 2 |
| C2×#19127896 | 2 |
| C2×#19127444 | 2 |
| #24905298 | 2 |
| C83×#1954 | 2 |
| #10260 | 83 |