Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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 | C23×C181 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C22×C4×C181 ◁ C22×C8×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #367×C181 | C2 | semidirect |
| 4. #366×C181 | C2 | semidirect |
| 5. #358×C181 | C2 | semidirect |
| 6. #358×C181 | C2 | semidirect |
| 65. C181 | #2237 | direct (N × H) |
| 66. #2237 | C181 | direct (N × H) |
| 69. #367 | C2×C181 | semidirect |
| 70. #366 | C2×C181 | semidirect |
| 71. #358 | C2×C181 | semidirect |
| 72. #358 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #467×C181 | 2 |
| #427×C181 | 2 |
| #367×C181 | 2 |
| #366×C181 | 2 |
| #358×C181 | 2 |
| C22⋊C16×C181 | 2 |
| #2237 | 181 |