Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
740 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 106 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, Frattini, cosocle | C2×C42 | C23×C23 |
| prime radical | C23×#2679 | C2 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2023 | C2 | semidirect |
| 3. C23×#2013 | C2 | semidirect |
| 4. C23×#1270 | C2 | semidirect |
| 5. C23×#1270 | C2 | semidirect |
| 7. C2×C23×C4⋊Q8 | C22 | semidirect |
| 17. C23×#336 | C22 | semidirect |
| 18. C23×#336 | C22 | semidirect |
| 72. C2×D4×C23 | SD16 | semidirect |
| 98. #7750 | C23 | direct (N × H) |
| 146. #2023 | C2×C23 | semidirect |
| 147. #2013 | C2×C23 | semidirect |
| 148. #1270 | C2×C23 | semidirect |
| 149. #1270 | C2×C23 | semidirect |
| 176. C2×C4⋊Q8 | C22×C23 | semidirect |
| 186. #336 | C22×C23 | semidirect |
| 187. #336 | C22×C23 | semidirect |
| 223. C23 | #7750 | direct (N × H) |
| 249. C2×D4 | SD16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2679 | 2 |
| C23×#2023 | 2 |
| C23×#2013 | 2 |
| C23×#1270 | 2 |
| #7750 | 23 |