Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
430 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 176 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 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C181 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C181 ◁ C2×C42×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #532×C181 | C2 | semidirect |
| 2. #476×C181 | C2 | semidirect |
| 3. #469×C181 | C2 | semidirect |
| 4. #459×C181 | C2 | semidirect |
| 5. #423×C181 | C2 | semidirect |
| 73. C181 | #3253 | direct (N × H) |
| 74. #3253 | C181 | direct (N × H) |
| 75. #532 | C2×C181 | semidirect |
| 76. #476 | C2×C181 | semidirect |
| 77. #469 | C2×C181 | semidirect |
| 78. #459 | C2×C181 | semidirect |
| 79. #423 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #532×C181 | 2 |
| #476×C181 | 2 |
| #469×C181 | 2 |
| #459×C181 | 2 |
| #423×C181 | 2 |
| #3253 | 181 |