Finite Group DatabasebetaFinite Group DatabasebetaOrder 8576.
382 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 92 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×C67 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C67 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C67 ◁ C22×C4×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×AGL(1,ℤ/8)×C67 | C2 | semidirect |
| 2. C22×D8×C67 | C2 | semidirect |
| 3. C2×#100×C67 | C2 | semidirect |
| 4. #408×C67 | C2 | semidirect |
| 5. #341×C67 | C2 | semidirect |
| 84. #2018 | C67 | direct (N × H) |
| 85. C67 | #2018 | direct (N × H) |
| 86. C2×AGL(1,ℤ/8) | C2×C67 | semidirect |
| 87. C22×D8 | C2×C67 | semidirect |
| 88. C2×#100 | C2×C67 | semidirect |
| 89. #408 | C2×C67 | semidirect |
| 90. #341 | C2×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×AGL(1,ℤ/8)×C67 | 2 |
| C22×D8×C67 | 2 |
| C2×#100×C67 | 2 |
| #408×C67 | 2 |
| #341×C67 | 2 |
| #2018 | 67 |