Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
740 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 105 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. #24918401 | C2 | semidirect |
| 3. #24906132 | C2 | semidirect |
| 4. #24905962 | C2 | semidirect |
| 5. #24905854 | C2 | semidirect |
| 6. #24905364 | C2 | semidirect |
| 7. C83×#3077 | C2 | semidirect |
| 47. C4⋊(C83⋊C8) | D4 | semidirect |
| 57. C4⋊Q8×C83 | D4 | semidirect |
| 58. C4⋊Q8×C83 | D4 | semidirect |
| 75. C4⋊C8×C83 | D4 | semidirect |
| 110. C2×D4×C83 | SD16 | semidirect |
| 223. #3077 | D83 | semidirect |
| 229. C83 | #10246 | semidirect |
| 261. C4⋊Q8 | C22⋊D83 | semidirect |
| 262. C4⋊Q8 | C22⋊D83 | semidirect |
| 291. C4⋊C8 | C22⋊D83 | semidirect |
| 324. C2×D4 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24918401 | 2 |
| #24912409 | 2 |
| #24906132 | 2 |
| #24905962 | 2 |
| #24905854 | 2 |
| #24905364 | 2 |
| C83×#3077 | 2 |
| #10246 | 83 |