Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
406 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 406 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 | C4×C8 | C23×C23 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C23×#436 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×#3273 | C2 | semidirect |
| 2. C23×#2250 | C2 | semidirect |
| 3. C23×#2206 | C2 | semidirect |
| 4. C23×#1687 | C2 | semidirect |
| 5. C23×#1360 | C2 | semidirect |
| 6. C23×#1333 | C2 | semidirect |
| 7. C23×#1330 | C2 | semidirect |
| 14. C23×#493 | C22 | semidirect |
| 22. C23×C4⋊C16 | C22 | semidirect |
| 24. C23×#346 | C22 | semidirect |
| 25. C23×#334 | C22 | semidirect |
| 95. D8×C23 | D8 | semidirect |
| 114. #12324 | C23 | direct (N × H) |
| 152. #3273 | C2×C23 | semidirect |
| 153. #2250 | C2×C23 | semidirect |
| 154. #2206 | C2×C23 | semidirect |
| 155. #1687 | C2×C23 | semidirect |
| 156. #1360 | C2×C23 | semidirect |
| 157. #1333 | C2×C23 | semidirect |
| 158. #1330 | C2×C23 | semidirect |
| 186. #493 | C22×C23 | semidirect |
| 194. C4⋊C16 | C22×C23 | semidirect |
| 196. #346 | C22×C23 | semidirect |
| 197. #334 | C22×C23 | semidirect |
| 244. C23 | #12324 | direct (N × H) |
| 275. D8 | D8×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3273 | 2 |
| C23×#2250 | 2 |
| C23×#2206 | 2 |
| C23×#1687 | 2 |
| C23×#1360 | 2 |
| C23×#1333 | 2 |
| C23×#1330 | 2 |
| #12324 | 23 |