Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
958 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 958 conjugacy classes of subgroups — too many to draw. Only its 130 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 | #386 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C23×#2404 | C2 |
| LCS | G ▷ C22×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×#2273 | C2 | semidirect |
| 3. C23×#1789 | C2 | semidirect |
| 4. C23×#1462 | C2 | semidirect |
| 5. C23×#1284 | C2 | semidirect |
| 12. C23×#393 | C4 | semidirect |
| 13. C23×#392 | C4 | semidirect |
| 25. C22×Q8×C23 | C2×C4 | semidirect |
| 28. C22×D4×C23 | C2×C4 | semidirect |
| 46. C2×C42×C23 | D4 | semidirect |
| 54. C23×#95 | C2×C4 | semidirect |
| 107. #9475 | C23 | direct (N × H) |
| 128. C23×C23 | #104 | semidirect |
| 162. #2273 | C2×C23 | semidirect |
| 163. #1789 | C2×C23 | semidirect |
| 164. #1462 | C2×C23 | semidirect |
| 165. #1284 | C2×C23 | semidirect |
| 202. #393 | C4×C23 | semidirect |
| 203. #392 | C4×C23 | semidirect |
| 223. C22×Q8 | C2×C4×C23 | semidirect |
| 226. C22×D4 | C2×C4×C23 | semidirect |
| 244. C2×C42 | D4×C23 | semidirect |
| 252. #95 | C2×C4×C23 | semidirect |
| 253. C23 | #9475 | direct (N × H) |
| 326. C23 | C23×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2404 | 2 |
| C23×#2273 | 2 |
| C23×#1789 | 2 |
| C23×#1462 | 2 |
| C23×#1284 | 2 |
| #9475 | 23 |