Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 84 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 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | C22×D4×C181 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C22×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #424×C181 | C2 | semidirect |
| 3. #419×C181 | C2 | semidirect |
| 5. C2×#101×C181 | C2 | semidirect |
| 7. #341×C181 | C2 | semidirect |
| 100. C181 | #2046 | direct (N × H) |
| 101. #2046 | C181 | direct (N × H) |
| 103. #424 | C2×C181 | semidirect |
| 104. #419 | C2×C181 | semidirect |
| 106. C2×#101 | C2×C181 | semidirect |
| 108. #341 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×SD16×C181 | 2 |
| #424×C181 | 2 |
| #419×C181 | 2 |
| #418×C181 | 2 |
| C2×#101×C181 | 2 |
| C2×#100×C181 | 2 |
| #341×C181 | 2 |
| #2046 | 181 |