Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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×#3199 | C2 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C23×#408 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2233 | C2 | semidirect |
| 3. C23×#2232 | C2 | semidirect |
| 4. C23×#2078 | C2 | semidirect |
| 5. C23×#1349 | C2 | semidirect |
| 6. C23×#1349 | C2 | semidirect |
| 7. C23×#1315 | C2 | semidirect |
| 16. C2×C23×#107 | C22 | semidirect |
| 23. C23×C22⋊C16 | C22 | semidirect |
| 24. C23×C22⋊C16 | C22 | semidirect |
| 26. C23×#341 | C22 | semidirect |
| 101. #12284 | C23 | direct (N × H) |
| 137. #2233 | C2×C23 | semidirect |
| 138. #2232 | C2×C23 | semidirect |
| 139. #2078 | C2×C23 | semidirect |
| 140. #1349 | C2×C23 | semidirect |
| 141. #1349 | C2×C23 | semidirect |
| 142. #1315 | C2×C23 | semidirect |
| 172. C2×#107 | C22×C23 | semidirect |
| 179. C22⋊C16 | C22×C23 | semidirect |
| 180. C22⋊C16 | C22×C23 | semidirect |
| 182. #341 | C22×C23 | semidirect |
| 223. C23 | #12284 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3199 | 2 |
| C23×#2233 | 2 |
| C23×#2232 | 2 |
| C23×#2078 | 2 |
| C23×#1349 | 2 |
| C23×#1315 | 2 |
| #12284 | 23 |