Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
528 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 82 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×#3186 | C2 | semidirect |
| 2. C23×#2184 | C2 | semidirect |
| 3. C23×#1999 | C2 | semidirect |
| 4. C23×#1347 | C2 | semidirect |
| 5. C23×#1314 | C2 | semidirect |
| 6. C22×D8×C23 | C22 | semidirect |
| 17. C23×C22⋊C16 | C22 | semidirect |
| 18. C23×#340 | C22 | semidirect |
| 27. C2×D8×C23 | D4 | semidirect |
| 43. C23×#107 | D4 | semidirect |
| 92. #12102 | C23 | direct (N × H) |
| 108. C23×C23 | D16 | semidirect |
| 137. #3186 | C2×C23 | semidirect |
| 138. #2184 | C2×C23 | semidirect |
| 139. #1999 | C2×C23 | semidirect |
| 140. #1347 | C2×C23 | semidirect |
| 141. #1314 | C2×C23 | semidirect |
| 169. C22×D8 | C22×C23 | semidirect |
| 180. C22⋊C16 | C22×C23 | semidirect |
| 181. #340 | C22×C23 | semidirect |
| 198. C2×D8 | D4×C23 | semidirect |
| 214. #107 | D4×C23 | semidirect |
| 219. C23 | #12102 | direct (N × H) |
| 279. C23 | C23×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3186 | 2 |
| C23×#2184 | 2 |
| C23×#1999 | 2 |
| C23×#1347 | 2 |
| C23×#1314 | 2 |
| #12102 | 23 |