Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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. #24923311 | C2 | semidirect |
| 4. #24923139 | C2 | semidirect |
| 5. #24923037 | C2 | semidirect |
| 6. #24923029 | C2 | semidirect |
| 25. #104×C167 | C4 | semidirect |
| 55. M16×C167 | C2×C4 | semidirect |
| 58. C42×C167 | C2×C4 | semidirect |
| 70. Q8×C167 | C4⋊C4 | semidirect |
| 74. D4×C167 | C4⋊C4 | semidirect |
| 112. C167 | #1859 | semidirect |
| 136. #104 | Dic167 | semidirect |
| 155. M16 | C2×Dic167 | semidirect |
| 171. C42 | C2×Dic167 | semidirect |
| 175. Q8 | C4⋊Dic167 | semidirect |
| 179. D4 | C4⋊Dic167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923752 | 2 |
| #24923311 | 2 |
| #24923270 | 2 |
| #24923139 | 2 |
| #24923037 | 2 |
| #24923029 | 2 |
| C2×#104×C167 | 2 |
| #1859 | 167 |