Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
592 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 224 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C83 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C83 |
| prime radical | C22×D4×C83 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C83 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C22⋊Q8×C83 | C2 | semidirect |
| 2. #396×C83 | C2 | semidirect |
| 3. #395×C83 | C2 | semidirect |
| 5. #389×C83 | C2 | semidirect |
| 27. C2×D4×C83 | Q8 | semidirect |
| 39. C4⋊C4×C83 | D4 | semidirect |
| 88. #2683 | C83 | direct (N × H) |
| 89. C83 | #2683 | direct (N × H) |
| 90. C2×C22⋊Q8 | C2×C83 | semidirect |
| 91. #396 | C2×C83 | semidirect |
| 92. #395 | C2×C83 | semidirect |
| 94. #389 | C2×C83 | semidirect |
| 116. C2×D4 | Q8×C83 | semidirect |
| 128. C4⋊C4 | D4×C83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊Q8×C83 | 2 |
| #396×C83 | 2 |
| #395×C83 | 2 |
| #390×C83 | 2 |
| #389×C83 | 2 |
| #386×C83 | 2 |
| #2683 | 83 |