Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19128766 | C2 | semidirect |
| 3. C2×#19128763 | C2 | semidirect |
| 6. #24923031 | C2 | semidirect |
| 7. #340×C167 | C2 | semidirect |
| 19. (C2×D167)⋊C8 | C4 | semidirect |
| 120. C167 | #1854 | semidirect |
| 128. #340 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128790 | 2 |
| C2×#19128766 | 2 |
| C2×#19128763 | 2 |
| C2×(C2×D167)⋊C8 | 2 |
| #24923126 | 2 |
| #24923031 | 2 |
| #340×C167 | 2 |
| #1854 | 167 |