Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
590 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 114 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C83 |
| prime radical | C22×D4×C83 | D4 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ C2×C42×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#501×C83 | C2 | semidirect |
| 4. C83×#1993 | C2 | semidirect |
| 5. C2×#330×C83 | C2 | semidirect |
| 7. C83×#1295 | C2 | semidirect |
| 188. #10082 | C83 | direct (N × H) |
| 195. C2×#501 | C2×C83 | semidirect |
| 198. #1993 | C2×C83 | semidirect |
| 199. C2×#330 | C2×C83 | semidirect |
| 201. #1295 | C2×C83 | semidirect |
| 202. C83 | #10082 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#501×C83 | 2 |
| C2×#497×C83 | 2 |
| C83×#2820 | 2 |
| C83×#1993 | 2 |
| C2×#330×C83 | 2 |
| C2×#329×C83 | 2 |
| C83×#1295 | 2 |
| #10082 | 83 |