Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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. #24920597 | C2 | semidirect |
| 2. #24917184 | C2 | semidirect |
| 3. #24917121 | C2 | semidirect |
| 4. C2×#19127512 | C2 | semidirect |
| 5. #24909092 | C2 | semidirect |
| 6. #24905563 | C2 | semidirect |
| 7. C83×#2143 | C2 | semidirect |
| 44. C2×Dic332 | D4 | semidirect |
| 46. C2×D664 | D4 | semidirect |
| 66. C2×C83⋊C16 | D4 | semidirect |
| 87. #108×C83 | D4 | semidirect |
| 231. #2143 | D83 | semidirect |
| 234. C83 | #13318 | semidirect |
| 308. #108 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24920597 | 2 |
| #24917184 | 2 |
| #24917121 | 2 |
| C2×#19127512 | 2 |
| #24909092 | 2 |
| #24905563 | 2 |
| C83×#2143 | 2 |
| #13318 | 83 |