Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 112 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 | C2×C4 | C22×C4×C181 |
| Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | C23×C181 | #41 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 10. C2×Q16×C181 | C4 | semidirect |
| 76. C181 | #1979 | direct (N × H) |
| 77. #1979 | C181 | direct (N × H) |
| 87. C2×Q16 | C4×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q16×C181 | 2 |
| C2×#108×C181 | 2 |
| #419×C181 | 2 |
| C2×#101×C181 | 2 |
| #405×C181 | 2 |
| #1979 | 181 |