Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C23 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×M16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3204 | C2 | semidirect |
| 2. C23×#2191 | C2 | semidirect |
| 3. C23×#2190 | C2 | semidirect |
| 4. C23×#2017 | C2 | semidirect |
| 5. C23×#1342 | C2 | semidirect |
| 6. C23×#1341 | C2 | semidirect |
| 7. C23×#1321 | C2 | semidirect |
| 126. #12119 | C23 | direct (N × H) |
| 166. #3204 | C2×C23 | semidirect |
| 167. #2191 | C2×C23 | semidirect |
| 168. #2190 | C2×C23 | semidirect |
| 169. #2017 | C2×C23 | semidirect |
| 170. #1342 | C2×C23 | semidirect |
| 171. #1341 | C2×C23 | semidirect |
| 172. #1321 | C2×C23 | semidirect |
| 260. C23 | #12119 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3204 | 2 |
| C23×#2191 | 2 |
| C23×#2190 | 2 |
| C23×#2017 | 2 |
| C23×#1342 | 2 |
| C23×#1341 | 2 |
| C23×#1321 | 2 |
| #12119 | 23 |