Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
198 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 80 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 | #127 |
| commutator, Frattini, cosocle | C42 | C23×C181 |
| prime radical | #127×C181 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #500×C181 | C2 | semidirect |
| 2. #498×C181 | C2 | semidirect |
| 5. #487×C181 | C2 | semidirect |
| 7. #322×C181 | C2 | semidirect |
| 54. C8×C181 | SD16 | semidirect |
| 69. C181 | #1714 | direct (N × H) |
| 70. #1714 | C181 | direct (N × H) |
| 71. #500 | C2×C181 | semidirect |
| 72. #498 | C2×C181 | semidirect |
| 75. #487 | C2×C181 | semidirect |
| 77. #322 | C2×C181 | semidirect |
| 124. C8 | SD16×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #500×C181 | 2 |
| #498×C181 | 2 |
| #492×C181 | 2 |
| #487×C181 | 2 |
| #486×C181 | 2 |
| #322×C181 | 2 |
| #1714 | 181 |