Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
124 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 124 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, prime radical | C22×C181 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C181 |
| 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 |
|---|---|---|
| 58. C181 | #2229 | direct (N × H) |
| 59. #2229 | C181 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×C181 | 2 |
| C4×Q16×C181 | 2 |
| #367×C181 | 2 |
| #366×C181 | 2 |
| C4⋊C16×C181 | 2 |
| #358×C181 | 2 |
| #2229 | 181 |