Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
370 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 83 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. #24923750 | C2 | semidirect |
| 3. C2×#19128758 | C2 | semidirect |
| 4. #24923275 | C2 | semidirect |
| 5. #24923170 | C2 | semidirect |
| 6. #24923030 | C2 | semidirect |
| 7. #343×C167 | C2 | semidirect |
| 11. #19128860 | C4 | semidirect |
| 39. C2×D668 | C2×C4 | semidirect |
| 62. M16×C167 | C2×C4 | semidirect |
| 74. Dic334 | C22⋊C4 | semidirect |
| 80. D668 | C22⋊C4 | semidirect |
| 132. C167 | #1883 | semidirect |
| 139. #343 | D167 | semidirect |
| 185. M16 | C4×D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128860 | 2 |
| #24923750 | 2 |
| C2×#19128758 | 2 |
| #24923275 | 2 |
| #24923170 | 2 |
| #24923030 | 2 |
| #343×C167 | 2 |
| #1883 | 167 |