Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
734 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 734 conjugacy classes of subgroups — too many to draw. Only its 169 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. C2×#19128099 | C2 | semidirect |
| 3. #24908424 | C2 | semidirect |
| 5. C83×#1273 | C2 | semidirect |
| 71. C2×C8×C83 | SD16 | semidirect |
| 72. C2×C8×C83 | SD16 | semidirect |
| 130. #1273 | D83 | semidirect |
| 131. C83 | #10315 | semidirect |
| 191. C2×C8 | #13050579 | semidirect |
| 192. C2×C8 | #13050579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19128099 | 2 |
| C2×#19128074 | 2 |
| #24908424 | 2 |
| #24908269 | 2 |
| C83×#1273 | 2 |
| #10315 | 83 |