Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
182 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C2×D4 |
| commutator | C2×C4 | C22×C4×C83 |
| Frattini, cosocle | C42 | C23×C83 |
| socle | C22×C83 | C4×D4 |
| prime radical | C2×D8×C83 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ C4×C8×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #436×C83 | C2 | semidirect |
| 3. C8×D4×C83 | C2 | semidirect |
| 4. #334×C83 | C2 | semidirect |
| 5. D4⋊C8×C83 | C2 | semidirect |
| 6. D4⋊C8×C83 | C2 | semidirect |
| 7. #322×C83 | C2 | semidirect |
| 47. D4×C83 | M16 | semidirect |
| 83. #1586 | C83 | direct (N × H) |
| 84. C83 | #1586 | direct (N × H) |
| 86. #436 | C2×C83 | semidirect |
| 87. C8×D4 | C2×C83 | semidirect |
| 88. #334 | C2×C83 | semidirect |
| 89. D4⋊C8 | C2×C83 | semidirect |
| 90. D4⋊C8 | C2×C83 | semidirect |
| 91. #322 | C2×C83 | semidirect |
| 131. D4 | M16×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D8×C83 | 2 |
| #436×C83 | 2 |
| C8×D4×C83 | 2 |
| #334×C83 | 2 |
| D4⋊C8×C83 | 2 |
| #322×C83 | 2 |
| #1586 | 83 |