Finite Group DatabasebetaFinite Group DatabasebetaOrder 5888.
360 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #418 |
| commutator | C2×C8 | C22×C4×C23 |
| Frattini, cosocle | C4×C8 | C23×C23 |
| socle | C2×C23 | #1490 |
| prime radical | C23×#575 | C4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C8×C23 ◁ C4×M16×C23 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#2165 | C2 | semidirect |
| 3. C23×#1455 | C2 | semidirect |
| 4. C23×#1336 | C2 | semidirect |
| 5. C23×#1335 | C2 | semidirect |
| 16. C23×#364 | C22 | semidirect |
| 20. C23×#322 | C22 | semidirect |
| 21. C82×C23 | C22 | semidirect |
| 59. Q16×C23 | M16 | semidirect |
| 63. D8×C23 | M16 | semidirect |
| 84. #11669 | C23 | direct (N × H) |
| 111. #2165 | C2×C23 | semidirect |
| 112. #1455 | C2×C23 | semidirect |
| 113. #1336 | C2×C23 | semidirect |
| 114. #1335 | C2×C23 | semidirect |
| 136. #364 | C22×C23 | semidirect |
| 140. #322 | C22×C23 | semidirect |
| 141. C82 | C22×C23 | semidirect |
| 172. C23 | #11669 | direct (N × H) |
| 184. Q16 | M16×C23 | semidirect |
| 188. D8 | M16×C23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#2956 | 2 |
| C23×#2165 | 2 |
| C23×#1455 | 2 |
| C23×#1336 | 2 |
| C23×#1335 | 2 |
| #11669 | 23 |