Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
462 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 1. #401×C181 | C2 | semidirect |
| 2. #400×C181 | C2 | semidirect |
| 3. #397×C181 | C2 | semidirect |
| 4. #396×C181 | C2 | semidirect |
| 6. #385×C181 | C2 | semidirect |
| 7. C2×#95×C181 | C2 | semidirect |
| 78. C181 | #2643 | direct (N × H) |
| 79. #2643 | C181 | direct (N × H) |
| 80. #401 | C2×C181 | semidirect |
| 81. #400 | C2×C181 | semidirect |
| 82. #397 | C2×C181 | semidirect |
| 83. #396 | C2×C181 | semidirect |
| 85. #385 | C2×C181 | semidirect |
| 86. C2×#95 | C2×C181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #401×C181 | 2 |
| #400×C181 | 2 |
| #397×C181 | 2 |
| #396×C181 | 2 |
| #386×C181 | 2 |
| #385×C181 | 2 |
| C2×#95×C181 | 2 |
| #2643 | 181 |