Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
1224 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | #120 |
| commutator | C22×C4 | C22×C4×C23 |
| Frattini, cosocle | C23×C4 | C23×C23 |
| prime radical | C2×C23×#392 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2312 | C2 | semidirect |
| 3. C23×#1786 | C2 | semidirect |
| 4. C2×C23×#323 | C2 | semidirect |
| 5. C23×#1294 | C2 | semidirect |
| 13. C23×#392 | C4 | semidirect |
| 35. C2×C4⋊C4×C23 | D4 | semidirect |
| 106. #9020 | C23 | direct (N × H) |
| 167. #2312 | C2×C23 | semidirect |
| 168. #1786 | C2×C23 | semidirect |
| 169. C2×#323 | C2×C23 | semidirect |
| 170. #1294 | C2×C23 | semidirect |
| 212. #392 | C4×C23 | semidirect |
| 243. C2×C4⋊C4 | D4×C23 | semidirect |
| 261. C23 | #9020 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C23×#392 | 2 |
| C23×#2312 | 2 |
| C23×#1786 | 2 |
| C2×C23×#323 | 2 |
| C23×#1294 | 2 |
| #9020 | 23 |