Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
354 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C83 | C2×#102 |
| commutator | C2×C8 | C22×C4×C83 |
| Frattini, cosocle | C4×C8 | C23×C83 |
| prime radical | C23×C83 | #102 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C2×C42×C83 ◁ C2×C4×C8×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C83×#1334 | C2 | semidirect |
| 112. #11668 | C83 | direct (N × H) |
| 120. #1334 | C2×C83 | semidirect |
| 121. C83 | #11668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q16×C83 | 2 |
| C83×#2163 | 2 |
| C83×#1568 | 2 |
| C83×#1334 | 2 |
| #11668 | 83 |