Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 96 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 | C22⋊C4 |
| commutator | C2×C4 | C42×C181 |
| Frattini, cosocle | C23×C4 | C22×C181 |
| prime radical | C24×C181 | D4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C181 ◁ C23×C4×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C2×C4⋊C4×C181 | C4 | semidirect |
| 10. C22⋊C8×C181 | C4 | semidirect |
| 13. #95×C181 | C4 | semidirect |
| 93. C181 | #1294 | direct (N × H) |
| 94. #1294 | C181 | direct (N × H) |
| 101. C2×C4⋊C4 | C4×C181 | semidirect |
| 104. C22⋊C8 | C4×C181 | semidirect |
| 107. #95 | C4×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C22⋊C8×C181 | 2 |
| #380×C181 | 2 |
| C2×#95×C181 | 2 |
| #1294 | 181 |