Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #24924005 | C2 | semidirect |
| 2. #24923993 | C2 | semidirect |
| 3. #24923650 | C2 | semidirect |
| 4. #24923489 | C2 | semidirect |
| 5. #24923486 | C2 | semidirect |
| 6. #24923476 | C2 | semidirect |
| 8. C8×Dic334 | C2 | semidirect |
| 9. C4×#14581939 | C2 | semidirect |
| 10. SD16×Dic167 | C2 | semidirect |
| 11. #492×C167 | C2 | semidirect |
| 125. C167 | #3394 | semidirect |
| 130. #492 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24924005 | 2 |
| #24923993 | 2 |
| #24923650 | 2 |
| #24923489 | 2 |
| #24923486 | 2 |
| #24923476 | 2 |
| #24923461 | 2 |
| C8×Dic334 | 2 |
| C4×#14581939 | 2 |
| SD16×Dic167 | 2 |
| #492×C167 | 2 |
| #3394 | 167 |