Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
180 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C83 | D4 |
| commutator | C4 | C22×C8×C83 |
| Frattini, cosocle | C42 | C23×C83 |
| socle | C22×C83 | C4×D4 |
| prime radical | C2×D4×C83 | C2×C4 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C83 ◁ C4×C8×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C8×Q8×C83 | C2 | semidirect |
| 4. #334×C83 | C2 | semidirect |
| 5. Q8⋊C8×C83 | C2 | semidirect |
| 7. C82×C83 | C2 | semidirect |
| 26. SD16×C83 | C8 | direct (N × H) |
| 43. Q8×C83 | C2×C8 | semidirect |
| 59. C8×C83 | C2×C8 | semidirect |
| 60. C8×C83 | SD16 | direct (N × H) |
| 77. C8×SD16 | C83 | direct (N × H) |
| 78. C83 | C8×SD16 | direct (N × H) |
| 79. C8×Q8 | C2×C83 | semidirect |
| 82. #334 | C2×C83 | semidirect |
| 83. Q8⋊C8 | C2×C83 | semidirect |
| 85. C82 | C2×C83 | semidirect |
| 104. SD16 | C8×C83 | direct (N × H) |
| 121. Q8 | C2×C8×C83 | semidirect |
| 137. C8 | C2×C8×C83 | semidirect |
| 138. C8 | SD16×C83 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×C83 | 2 |
| C4×SD16×C83 | 2 |
| C8×D4×C83 | 2 |
| #334×C83 | 2 |
| Q8⋊C8×C83 | 2 |
| D4⋊C8×C83 | 2 |
| C82×C83 | 2 |
| C8×SD16 | 83 |