Finite Group DatabasebetaFinite Group DatabasebetaOrder 21248.
230 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 230 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, socle | C22×C83 | #442 |
| commutator | C8 | C22×C8×C83 |
| Frattini, cosocle | C4×C8 | C23×C83 |
| prime radical | C2×D8×C83 | C2×C4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C83 ◁ C42×C83 ◁ #322×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C83×#1579 | C2 | semidirect |
| 4. C83×#1368 | C2 | semidirect |
| 5. C83×#1334 | C2 | semidirect |
| 7. C83×#1313 | C2 | semidirect |
| 28. SD32×C83 | C8 | semidirect |
| 48. Q16×C83 | C2×C8 | semidirect |
| 66. C16×C83 | C2×C8 | semidirect |
| 98. #12065 | C83 | direct (N × H) |
| 105. #1579 | C2×C83 | semidirect |
| 106. #1368 | C2×C83 | semidirect |
| 107. #1334 | C2×C83 | semidirect |
| 109. #1313 | C2×C83 | semidirect |
| 110. C83 | #12065 | direct (N × H) |
| 131. SD32 | C8×C83 | semidirect |
| 151. Q16 | C2×C8×C83 | semidirect |
| 169. C16 | C2×C8×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C83×#2175 | 2 |
| C83×#1580 | 2 |
| C83×#1579 | 2 |
| C83×#1368 | 2 |
| C83×#1334 | 2 |
| C83×#1333 | 2 |
| C83×#1313 | 2 |
| #12065 | 83 |