Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
582 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 216 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 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C181 |
| prime radical | C22×D4×C181 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C181 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42×C181 | C2 | semidirect |
| 3. #388×C181 | C2 | semidirect |
| 4. #387×C181 | C2 | semidirect |
| 6. #385×C181 | C2 | semidirect |
| 7. #381×C181 | C2 | semidirect |
| 84. C181 | #2853 | direct (N × H) |
| 85. #2853 | C181 | direct (N × H) |
| 87. C22×C42 | C2×C181 | semidirect |
| 88. #388 | C2×C181 | semidirect |
| 89. #387 | C2×C181 | semidirect |
| 91. #385 | C2×C181 | semidirect |
| 92. #381 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#123×C181 | 2 |
| C22×C42×C181 | 2 |
| #388×C181 | 2 |
| #387×C181 | 2 |
| #386×C181 | 2 |
| #385×C181 | 2 |
| #381×C181 | 2 |
| #2853 | 181 |