Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
464 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 94 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×C23 | #394 |
| commutator, Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C2×C23×#121 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#1901 | C2 | semidirect |
| 4. C23×#1855 | C2 | semidirect |
| 5. C23×#1520 | C2 | semidirect |
| 7. C23×#1305 | C2 | semidirect |
| 131. #10561 | C23 | direct (N × H) |
| 180. #1901 | C2×C23 | semidirect |
| 182. #1855 | C2×C23 | semidirect |
| 183. #1520 | C2×C23 | semidirect |
| 185. #1305 | C2×C23 | semidirect |
| 287. C23 | #10561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3193 | 2 |
| C23×#1901 | 2 |
| C23×#1895 | 2 |
| C23×#1855 | 2 |
| C23×#1520 | 2 |
| C23×#1471 | 2 |
| C23×#1305 | 2 |
| #10561 | 23 |