Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
500 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×#99 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C23 |
| prime radical | C23×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C4×D4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C4×C23×#99 | C2 | semidirect |
| 3. C23×#1459 | C2 | semidirect |
| 4. C23×#1351 | C2 | semidirect |
| 5. C23×#1343 | C2 | semidirect |
| 6. C2×C23×#124 | C4 | semidirect |
| 11. C23×#393 | C4 | semidirect |
| 14. C23×#392 | C4 | semidirect |
| 18. C23×#383 | C4 | semidirect |
| 105. #11730 | C23 | direct (N × H) |
| 159. C4×#99 | C2×C23 | semidirect |
| 160. #1459 | C2×C23 | semidirect |
| 161. #1351 | C2×C23 | semidirect |
| 162. #1343 | C2×C23 | semidirect |
| 195. C2×#124 | C4×C23 | semidirect |
| 200. #393 | C4×C23 | semidirect |
| 203. #392 | C4×C23 | semidirect |
| 207. #383 | C4×C23 | semidirect |
| 254. C23 | #11730 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2631 | 2 |
| C4×C23×#99 | 2 |
| C23×#1459 | 2 |
| C23×#1351 | 2 |
| C23×#1343 | 2 |
| #11730 | 23 |