Finite Group DatabasebetaFinite Group DatabasebetaOrder 10112.
644 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 184 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×C79 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C79 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#121×C79 | C2 | semidirect |
| 2. #397×C79 | C2 | semidirect |
| 3. #392×C79 | C2 | semidirect |
| 4. #392×C79 | C2 | semidirect |
| 5. #381×C79 | C2 | semidirect |
| 26. C22×C4×C79 | D4 | semidirect |
| 72. #2815 | C79 | direct (N × H) |
| 73. C79 | #2815 | direct (N × H) |
| 74. C2×#121 | C2×C79 | semidirect |
| 75. #397 | C2×C79 | semidirect |
| 76. #392 | C2×C79 | semidirect |
| 77. #392 | C2×C79 | semidirect |
| 78. #381 | C2×C79 | semidirect |
| 99. C22×C4 | D4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#121×C79 | 2 |
| #397×C79 | 2 |
| #392×C79 | 2 |
| #381×C79 | 2 |
| #2815 | 79 |