Finite Group DatabasebetaFinite Group DatabasebetaOrder 21376.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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. #24923892 | C2 | semidirect |
| 2. #24923666 | C2 | semidirect |
| 3. #24923654 | C2 | semidirect |
| 4. #24923630 | C2 | semidirect |
| 6. #24923500 | C2 | semidirect |
| 7. #24923380 | C2 | semidirect |
| 8. #24923376 | C2 | semidirect |
| 9. #24923354 | C2 | semidirect |
| 10. #24923227 | C2 | semidirect |
| 11. #470×C167 | C2 | semidirect |
| 109. C167 | #3173 | semidirect |
| 115. #470 | D167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24923892 | 2 |
| #24923666 | 2 |
| #24923654 | 2 |
| #24923630 | 2 |
| #24923522 | 2 |
| #24923500 | 2 |
| #24923380 | 2 |
| #24923376 | 2 |
| #24923354 | 2 |
| #24923227 | 2 |
| #470×C167 | 2 |
| #3173 | 167 |