Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
564 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#3205 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3208 | C2 | semidirect |
| 3. C23×#3135 | C2 | semidirect |
| 4. C23×#1961 | C2 | semidirect |
| 5. C23×#1518 | C2 | semidirect |
| 6. C23×#1517 | C2 | semidirect |
| 7. C23×#1281 | C2 | semidirect |
| 125. #10219 | C23 | direct (N × H) |
| 167. #3208 | C2×C23 | semidirect |
| 169. #3135 | C2×C23 | semidirect |
| 170. #1961 | C2×C23 | semidirect |
| 171. #1518 | C2×C23 | semidirect |
| 172. #1517 | C2×C23 | semidirect |
| 173. #1281 | C2×C23 | semidirect |
| 272. C23 | #10219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3208 | 2 |
| C23×#3205 | 2 |
| C23×#3135 | 2 |
| C23×#1961 | 2 |
| C23×#1518 | 2 |
| C23×#1517 | 2 |
| C23×#1281 | 2 |
| #10219 | 23 |