Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
480 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C23 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C2×C23×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3191 | C2 | semidirect |
| 2. C23×#2187 | C2 | semidirect |
| 3. C23×#2184 | C2 | semidirect |
| 4. C23×#1999 | C2 | semidirect |
| 5. C23×#1348 | C2 | semidirect |
| 6. C23×#1347 | C2 | semidirect |
| 7. C23×#1314 | C2 | semidirect |
| 31. C2×Q16×C23 | D4 | semidirect |
| 36. C2×D8×C23 | D4 | semidirect |
| 56. C23×#107 | D4 | semidirect |
| 57. C23×#107 | D4 | semidirect |
| 119. #12104 | C23 | direct (N × H) |
| 166. #3191 | C2×C23 | semidirect |
| 167. #2187 | C2×C23 | semidirect |
| 168. #2184 | C2×C23 | semidirect |
| 169. #1999 | C2×C23 | semidirect |
| 170. #1348 | C2×C23 | semidirect |
| 171. #1347 | C2×C23 | semidirect |
| 172. #1314 | C2×C23 | semidirect |
| 232. C2×Q16 | D4×C23 | semidirect |
| 237. C2×D8 | D4×C23 | semidirect |
| 257. #107 | D4×C23 | semidirect |
| 258. #107 | D4×C23 | semidirect |
| 267. C23 | #12104 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3191 | 2 |
| C23×#2187 | 2 |
| C23×#2184 | 2 |
| C23×#1999 | 2 |
| C23×#1348 | 2 |
| C23×#1347 | 2 |
| C23×#1314 | 2 |
| #12104 | 23 |