Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
440 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | #99 |
| commutator | C22×C4 | C22×C4×C83 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C83 |
| socle | C22×C83 | C2×#99 |
| prime radical | C22×D4×C83 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C22×C4×C83 ◁ C2×C4×D4×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C83×#1353 | C2 | semidirect |
| 5. C83×#1346 | C2 | semidirect |
| 165. #11735 | C83 | direct (N × H) |
| 176. #1353 | C2×C83 | semidirect |
| 177. #1346 | C2×C83 | semidirect |
| 178. C83 | #11735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C83×#2395 | 2 |
| C4×#100×C83 | 2 |
| C83×#1459 | 2 |
| C83×#1353 | 2 |
| C83×#1346 | 2 |
| #11735 | 83 |