Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
274 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C181 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C181 |
| prime radical | C22×D4×C181 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C181 ◁ C2×C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #384×C181 | C2 | semidirect |
| 4. #340×C181 | C2 | semidirect |
| 5. #336×C181 | C2 | semidirect |
| 92. C181 | #2071 | direct (N × H) |
| 93. #2071 | C181 | direct (N × H) |
| 96. #384 | C2×C181 | semidirect |
| 97. #340 | C2×C181 | semidirect |
| 98. #336 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#102×C181 | 2 |
| #390×C181 | 2 |
| #384×C181 | 2 |
| #340×C181 | 2 |
| #336×C181 | 2 |
| #2071 | 181 |