Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
348 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2127 |
| commutator | C42 | C22×C4×C23 |
| Frattini, cosocle | #127 | C23×C23 |
| prime radical | C23×#3220 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C23 ◁ C22×C4×C23 ◁ C23×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2128 | C2 | semidirect |
| 3. C23×#2127 | C2 | semidirect |
| 4. C23×#1412 | C2 | semidirect |
| 5. C23×#1408 | C2 | semidirect |
| 6. C23×#540 | C4 | semidirect |
| 8. C23×#496 | C4 | semidirect |
| 11. C23×#488 | C4 | semidirect |
| 16. C23×#433 | C4 | semidirect |
| 29. C23×#127 | C2×C4 | semidirect |
| 32. C23×#125 | C2×C4 | semidirect |
| 54. C23×#97 | C2×C4 | semidirect |
| 55. C4×C8×C23 | C2×C4 | semidirect |
| 95. #13609 | C23 | direct (N × H) |
| 132. #2128 | C2×C23 | semidirect |
| 133. #2127 | C2×C23 | semidirect |
| 134. #1412 | C2×C23 | semidirect |
| 135. #1408 | C2×C23 | semidirect |
| 158. #540 | C4×C23 | semidirect |
| 160. #496 | C4×C23 | semidirect |
| 163. #488 | C4×C23 | semidirect |
| 168. #433 | C4×C23 | semidirect |
| 188. #127 | C2×C4×C23 | semidirect |
| 191. #125 | C2×C4×C23 | semidirect |
| 213. #97 | C2×C4×C23 | semidirect |
| 214. C4×C8 | C2×C4×C23 | semidirect |
| 215. C23 | #13609 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#3220 | 2 |
| C23×#2128 | 2 |
| C23×#2127 | 2 |
| C23×#1412 | 2 |
| C23×#1408 | 2 |
| #13609 | 23 |