Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
392 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 392 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. Q8×Dic334 | C2 | semidirect |
| 3. #24923616 | C2 | semidirect |
| 4. #24923560 | C2 | semidirect |
| 5. #24923470 | C2 | semidirect |
| 6. C4×#14581939 | C2 | semidirect |
| 7. C8×Q8×C167 | C2 | semidirect |
| 46. Dic334 | #41 | semidirect |
| 55. Q8×C167 | SD16 | semidirect |
| 76. C167 | #3362 | semidirect |
| 83. C8×Q8 | D167 | semidirect |
| 124. Q8 | #14581939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic334 | 2 |
| #24923941 | 2 |
| #24923616 | 2 |
| #24923560 | 2 |
| #24923470 | 2 |
| C4×#14581939 | 2 |
| C8×Q8×C167 | 2 |
| #3362 | 167 |