Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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×C181 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C181 |
| prime radical | C2×D16×C181 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C42×C181 ◁ C4×C8×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×SD32×C181 | C2 | semidirect |
| 3. #495×C181 | C2 | semidirect |
| 4. C4×D8×C181 | C2 | semidirect |
| 5. C4⋊C16×C181 | C2 | semidirect |
| 6. #358×C181 | C2 | semidirect |
| 7. #357×C181 | C2 | semidirect |
| 76. C181 | #2210 | direct (N × H) |
| 77. #2210 | C181 | direct (N × H) |
| 78. C2×SD32 | C2×C181 | semidirect |
| 80. #495 | C2×C181 | semidirect |
| 81. C4×D8 | C2×C181 | semidirect |
| 82. C4⋊C16 | C2×C181 | semidirect |
| 83. #358 | C2×C181 | semidirect |
| 84. #357 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD32×C181 | 2 |
| C2×D16×C181 | 2 |
| #495×C181 | 2 |
| C4×D8×C181 | 2 |
| C4⋊C16×C181 | 2 |
| #358×C181 | 2 |
| #357×C181 | 2 |
| #2210 | 181 |