Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
428 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C23 |
| prime radical | C23×#3191 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2188 | C2 | semidirect |
| 3. C23×#2185 | C2 | semidirect |
| 4. C23×#2001 | C2 | semidirect |
| 5. C23×#1348 | C2 | semidirect |
| 6. C23×#1347 | C2 | semidirect |
| 7. C23×#1314 | C2 | semidirect |
| 117. #12107 | C23 | direct (N × H) |
| 160. #2188 | C2×C23 | semidirect |
| 161. #2185 | C2×C23 | semidirect |
| 162. #2001 | C2×C23 | semidirect |
| 163. #1348 | C2×C23 | semidirect |
| 164. #1347 | C2×C23 | semidirect |
| 165. #1314 | C2×C23 | semidirect |
| 253. C23 | #12107 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3191 | 2 |
| C23×#2188 | 2 |
| C23×#2185 | 2 |
| C23×#2001 | 2 |
| C23×#1348 | 2 |
| C23×#1347 | 2 |
| C23×#1314 | 2 |
| #12107 | 23 |