Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
380 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 69 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. #24924069 | C2 | semidirect |
| 2. C2×#19128858 | C2 | semidirect |
| 3. #24923836 | C2 | semidirect |
| 4. #24923287 | C2 | semidirect |
| 5. #24923242 | C2 | semidirect |
| 6. #24923040 | C2 | semidirect |
| 7. #418×C167 | C2 | semidirect |
| 40. C2×Dic334 | D4 | semidirect |
| 42. C2×D668 | D4 | semidirect |
| 55. #14581934 | D4 | semidirect |
| 71. C2×C8×C167 | D4 | semidirect |
| 142. C167 | #2008 | semidirect |
| 148. #418 | D167 | semidirect |
| 210. C2×C8 | C22⋊D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924069 | 2 |
| C2×#19128858 | 2 |
| #24923836 | 2 |
| #24923287 | 2 |
| #24923242 | 2 |
| #24923040 | 2 |
| #418×C167 | 2 |
| #2008 | 167 |