Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. C2×#19127534 | C2 | semidirect |
| 3. C22⋊(C83⋊C32) | C2 | semidirect |
| 4. (C2×D83)⋊C32 | C2 | semidirect |
| 5. C83×C22⋊C32 | C2 | semidirect |
| 14. C2×C83⋊C32 | C22 | semidirect |
| 16. C2×C32×C83 | C22 | semidirect |
| 90. C22×C83 | M64 | semidirect |
| 98. C2×D83 | M64 | semidirect |
| 115. C22⋊C32 | D83 | semidirect |
| 116. C83 | #13553 | semidirect |
| 127. C2×C32 | C2×D83 | semidirect |
| 208. C22 | #19127534 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D83 | 2 |
| C2×#19127534 | 2 |
| C22⋊(C83⋊C32) | 2 |
| (C2×D83)⋊C32 | 2 |
| C83×C22⋊C32 | 2 |
| #13553 | 83 |